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Liang Z, Wang S, Cai L. Optimal model averaging for partially linear models with missing response variables and error-prone covariates. Stat Med 2024. [PMID: 39054668 DOI: 10.1002/sim.10176] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2024] [Revised: 05/22/2024] [Accepted: 07/10/2024] [Indexed: 07/27/2024]
Abstract
We consider the problem of optimal model averaging for partially linear models when the responses are missing at random and some covariates are measured with error. A novel weight choice criterion based on the Mallows-type criterion is proposed for the weight vector to be used in the model averaging. The resulting model averaging estimator for the partially linear models is shown to be asymptotically optimal under some regularity conditions in terms of achieving the smallest possible squared loss. In addition, the existence of a local minimizing weight vector and its convergence rate to the risk-based optimal weight vector are established. Simulation studies suggest that the proposed model averaging method generally outperforms existing methods. As an illustration, the proposed method is applied to analyze an HIV-CD4 dataset.
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Affiliation(s)
- Zhongqi Liang
- School of Data Sciences, Zhejiang University of Finance & Economics, Hangzhou, China
- School of Computer and Computing Science, Hangzhou City University, Hangzhou, China
| | - Suojin Wang
- Department of Statistics, Texas A&M University, College Station, Texas
| | - Li Cai
- School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, China
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2
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Aydın D, Yılmaz E, Chamidah N, Lestari B. Right-censored partially linear regression model with error in variables: application with carotid endarterectomy dataset. Int J Biostat 2024; 20:245-278. [PMID: 37257507 DOI: 10.1515/ijb-2022-0044] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2022] [Accepted: 05/11/2023] [Indexed: 06/02/2023]
Abstract
This paper considers a partially linear regression model relating a right-censored response variable to predictors and an extra covariate with measured error. The main problem here is that censorship and measurement error problems need to be solved to estimate the model correctly. In this sense, we propose three modified semiparametric estimators obtained from local polynomial regression, kernel smoothing, and B-spline smoothing methods based on kernel deconvolution approach and synthetic data transformation. Here, kernel deconvolution technique is used to solve the measurement error problem in the model and synthetic data transformation is considered to add the effect of censorship to the estimation procedure, which is a very common method in the literature. The performances of the introduced estimators are compared in the detailed Monte-Carlo simulation study. In addition, Carotid endarterectomy data is used as real-world data example and results are presented. According to the results, it is seen that the deconvoluted local polynomial method gives more qualified estimates than other two methods.
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Affiliation(s)
- Dursun Aydın
- Department of Statistics, Faculty of Science, Mugla Sitki Kocman University, Mugla, Türkiye
| | - Ersin Yılmaz
- Department of Statistics, Faculty of Science, Mugla Sitki Kocman University, Mugla, Türkiye
| | - Nur Chamidah
- Department of Mathematics, Faculty of Science and Technology, Airlangaa University, Surabaya, Indonesia
| | - Budi Lestari
- Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Jember, Jember, Indonesia
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3
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Jones J, Ertefaie A, Shortreed SM. Rejoinder to "Reader reaction to 'Outcome-adaptive Lasso: Variable selection for causal inference' by Shortreed and Ertefaie (2017)". Biometrics 2023; 79:521-525. [PMID: 35579597 PMCID: PMC9669282 DOI: 10.1111/biom.13681] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 04/19/2022] [Indexed: 11/28/2022]
Affiliation(s)
- Jeremiah Jones
- Department of Biostatistics and Computational Biology, University of Rochester, Rochester, New York, USA
| | - Ashkan Ertefaie
- Department of Biostatistics and Computational Biology, University of Rochester, Rochester, New York, USA
| | - Susan M Shortreed
- Biostatistics Division, Kaiser Permanente Washington Health Research Institute, Seattle, Washington, USA
- Department of Biostatistics, Univerisity of Washington, Seattle, Washington, USA
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4
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Ahmed SE, Aydın D, Yılmaz E. Penalty and Shrinkage Strategies Based on Local Polynomials for Right-Censored Partially Linear Regression. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1833. [PMID: 36554238 PMCID: PMC9778259 DOI: 10.3390/e24121833] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Revised: 12/08/2022] [Accepted: 12/13/2022] [Indexed: 06/17/2023]
Abstract
This study aims to propose modified semiparametric estimators based on six different penalty and shrinkage strategies for the estimation of a right-censored semiparametric regression model. In this context, the methods used to obtain the estimators are ridge, lasso, adaptive lasso, SCAD, MCP, and elasticnet penalty functions. The most important contribution that distinguishes this article from its peers is that it uses the local polynomial method as a smoothing method. The theoretical estimation procedures for the obtained estimators are explained. In addition, a simulation study is performed to see the behavior of the estimators and make a detailed comparison, and hepatocellular carcinoma data are estimated as a real data example. As a result of the study, the estimators based on adaptive lasso and SCAD were more resistant to censorship and outperformed the other four estimators.
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Affiliation(s)
- Syed Ejaz Ahmed
- Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S 3A1, Canada
| | - Dursun Aydın
- Department of Statistics, Mugla Sıtkı Kocman University, 48000 Mugla, Turkey
| | - Ersin Yılmaz
- Department of Statistics, Mugla Sıtkı Kocman University, 48000 Mugla, Turkey
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5
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Chokri K, Bouzebda S. Uniform-in-bandwidth consistency results in the partially linear additive model components estimation. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2022.2153605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Khalid Chokri
- M.A.E.G.E. Laboratory, Hassan II University of Casablanca, Casablanca, Morocco
| | - Salim Bouzebda
- LMAC (Laboratory of Applied Mathematics of Compiègne), Université de technologie de Compiègne, Compiègne Cedex, France
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6
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Reich BJ, Yang S, Guan Y. Discussion on "Spatial+: A novel approach to spatial confounding" by Dupont, Wood, and Augustin. Biometrics 2022; 78:1291-1294. [PMID: 35352823 PMCID: PMC10855624 DOI: 10.1111/biom.13651] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2021] [Revised: 07/12/2021] [Accepted: 07/16/2021] [Indexed: 12/30/2022]
Affiliation(s)
- Brian J. Reich
- Department of Statistics, North Carolina State University, Raleigh, North Carolina, USA
| | - Shu Yang
- Department of Statistics, North Carolina State University, Raleigh, North Carolina, USA
| | - Yawen Guan
- Department of Statistics, University of Nebraska-Lincoln, Lincoln, Nebraska, USA
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7
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Rodríguez D, Valdora M, Vena P. Robust estimation in partially linear regression models with monotonicity constraints. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2019.1691732] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Daniela Rodríguez
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Instituto de Cálculo, Buenos Aires, Argentina
- CONICET, Buenos Aires, Argentina
| | - Marina Valdora
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Instituto de Cálculo, Buenos Aires, Argentina
| | - Pablo Vena
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Instituto de Cálculo, Buenos Aires, Argentina
- CONICET, Buenos Aires, Argentina
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8
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Semiparametric Time-Series Model Using Local Polynomial: An Application on the Effects of Financial Risk Factors on Crop Yield. JOURNAL OF RISK AND FINANCIAL MANAGEMENT 2022. [DOI: 10.3390/jrfm15030141] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This paper proposes a semiparametric local polynomial estimator for modelling agricultural time-series. We consider the modelling of the crop yield variable according to determined financial risk factors in Turkey. The derivation of a semiparametric local polynomial estimator is provided with its fundamental statistical properties to estimate the semiparametric time-series model. This paper attaches importance to precision agriculture (PA) and therefore a local polynomial technique is considered due to some advantages it has over alternative methods. The introduced estimator provides less estimation risk, involving both parametric and nonparametric components that allow the estimator to represent the data structure better. From that, it can be said that the proposed estimator and model is beneficial to agricultural researchers for financial decision-making processes.
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9
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Affiliation(s)
- Seloua Boukabour
- Probability and Statistics Laboratory, Faculty of Sciences, Sfax University, Sfax, Tunisia
| | - Afif Masmoudi
- Probability and Statistics Laboratory, Faculty of Sciences, Sfax University, Sfax, Tunisia
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10
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Yenilmez İ, Yılmaz E, Kantar YM, Aydın D. Comparison of parametric and semi-parametric models with randomly right-censored data by weighted estimators: Two applications in colon cancer and hepatocellular carcinoma datasets. Stat Methods Med Res 2021; 31:372-387. [PMID: 34903099 DOI: 10.1177/09622802211061635] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this study, parametric and semi-parametric regression models are examined for random right censorship. The components of the aforementioned regression models are estimated with weights based on Cox and Kaplan-Meier estimates, which are semi-parametric and nonparametric methods used in survival analysis, respectively. The Tobit based on weights obtained from a Cox regression is handled as a parametric model instead of other parametric models requiring distribution assumptions such as exponential, Weibull, and gamma distributions. Also, the semi-parametric smoothing spline and the semi-parametric smoothing kernel estimators based on Kaplan-Meier weights are used. Therefore, estimates are obtained from two models with flexible approaches. To show the flexible shape of the models depending on the weights, Monte Carlo simulations are conducted, and all results are presented and discussed. Two empirical datasets are used to show the performance of the aforementioned estimators. Although three approaches gave similar results to each other, the semi-parametric approach was slightly superior to the parametric approach. The parametric approach method, on the other hand, yields good results in medium and large sample sizes and at a high censorship level. All other findings have been shared and interpreted.
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Affiliation(s)
- İsmail Yenilmez
- Department of Statistics, 522675Eskişehir Technical University, Eskişehir, Turkey
| | - Ersin Yılmaz
- Department of Statistics, 52986Muğla Sitki Koçman University, Muğla, Turkey
| | - Yeliz Mert Kantar
- Department of Statistics, 522675Eskişehir Technical University, Eskişehir, Turkey
| | - Dursun Aydın
- Department of Statistics, 52986Muğla Sitki Koçman University, Muğla, Turkey
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11
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Zou Y, Wu C, Fan G, Zhang R. Jackknife empirical likelihood of error variance for partially linear varying-coefficient model with missing covariates. COMMUN STAT-THEOR M 2021. [DOI: 10.1080/03610926.2021.1938128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Yuye Zou
- College of Economics and Management, Shanghai Maritime University, Shanghai, China
- Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE, School of Statistics, East China Normal University, Shanghai, China
| | - Chengxin Wu
- School of Mathematics, Hefei University of Technology, Hefei, China
- School of Mathematics and Statistics, Huangshan University, Huangshan, China
| | - Guoliang Fan
- College of Economics and Management, Shanghai Maritime University, Shanghai, China
| | - Riquan Zhang
- Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE, School of Statistics, East China Normal University, Shanghai, China
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12
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Jeon JM, Park BU, Van Keilegom I. Additive regression for predictors of various natures and possibly incomplete Hilbertian responses. Electron J Stat 2021. [DOI: 10.1214/21-ejs1823] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
| | - Byeong U. Park
- Department of Statistics, Seoul National University Gwanak-ro 1, Seoul 08826, South Korea
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13
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Emmenegger C, Bühlmann P. Regularizing double machine learning in partially linear endogenous models. Electron J Stat 2021. [DOI: 10.1214/21-ejs1931] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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14
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The Environmental Kuznets Curve: A Semiparametric Approach with Cross-Sectional Dependence. JOURNAL OF RISK AND FINANCIAL MANAGEMENT 2020. [DOI: 10.3390/jrfm13110292] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
This paper proposes a new approach to examine the relationship between CO2 emissions and economic developing. In particular, we propose to test the Environmental Kuznets Curve (EKC) hypothesis for a panel of 24 OECD countries and 32 non-OECD countries by developing a more flexible estimation technique which enables to account for functional form misspecification, cross-sectional dependence, and heterogeneous relationships among variables, simultaneously. We propose a new nonparametric estimator that extends the well-known Common Correlated Effect (CCE) approach from a fully parametric framework to a semiparametric panel data model. Our results corroborates that the nature and validity of the income–pollution relationship based on the EKC hypothesis depends on the model assumptions about the functional form specification. For all the countries analyzed, the proposed semiparametric estimator leads to non-monotonically increasing or decreasing relationships for CO2 emissions, depending on the level of economic development of the country.
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15
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Wang S, Cui H. Test for high dimensional regression coefficients of partially linear models. COMMUN STAT-THEOR M 2020. [DOI: 10.1080/03610926.2019.1594293] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Siyang Wang
- Department of Mathematical Statistics, School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China
| | - Hengjian Cui
- Department of Statistics, School of Mathematical Sciences, Capital Normal University, Beijing, China
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16
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The Consistency of Estimators in a Heteroscedastic Partially Linear Model with ρ−-Mixing Errors. Symmetry (Basel) 2020. [DOI: 10.3390/sym12071188] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
This paper studies a heteroscedastic partially linear model based on ρ − -mixing random errors, stochastically dominated and with zero mean. Under some suitable conditions, the strong consistency and p -th ( p > 0 ) mean consistency of least squares (LS) estimators and weighted least squares (WLS) estimators for the unknown parameter are investigated, and the strong consistency and p -th ( p > 0 ) mean consistency of the estimators for the non-parametric component are also studied. These results include the corresponding ones of independent, negatively associated (NA), and ρ * -mixing random errors as special cases. At last, two simulations are presented to support the theoretical results.
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17
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Phukongtong S, Lisawadi S, Ahmed SE. Penalty, post pretest and shrinkage strategies in a partially linear model. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2020.1788589] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Siwaporn Phukongtong
- Department of Mathematics and Statistics, Thammasat University, Pathum Thani, Thailand
| | - Supranee Lisawadi
- Department of Mathematics and Statistics, Thammasat University, Pathum Thani, Thailand
| | - S. Ejaz Ahmed
- Department of Mathematics and Statistics, Brock University, St. Catharines, ON, Canada
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18
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Spatial Analysis of Housing Prices and Market Activity with the Geographically Weighted Regression. ISPRS INTERNATIONAL JOURNAL OF GEO-INFORMATION 2020. [DOI: 10.3390/ijgi9060380] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The main part of the study will be to demonstrate that models taking into account spatial heterogeneity (Geographically Weighted Regression and Mixed Geographically Weighted Regression) which reproduce housing market determinants better reflect market relationships than conventional regression models. The spatial heterogeneity of the housing market determinants results in the spatial diversity of the market activity, as well as of real estate prices and values. The main aim of the study was to analyse an effect of these socio-demographic and environmental factors on average housing property prices and on the number of transactions in a spatial approach. In previous research conducted on a national scale, usually all variables were treated in a similar way, i.e., as global or local variables. During the research, an attempt was also made to answer the question of which of the variables adopted for analysis have a local impact on prices and market activity, and which are global. The study was conducted in Poland and used data from the year 2018 on 380 counties (Local Administrative Units). The study showed that determinants both for average prices and for the housing market activity show spatial autocorrelation with high–high and low–low cluster groups. Owing to these models, it was possible to draw specific conclusions on local determinants of flat prices and the market activity in Poland. The study findings have confirmed that they are an extremely effective tool for spatial data analysis.
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19
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Ye Z, Huang Z, Ding H. Adaptive structure inferences on partially linear error-in-function models with error-prone covariates. J Korean Stat Soc 2020. [DOI: 10.1007/s42952-019-00012-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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20
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Shimizu Y, Hoshino T. Doubly robust‐type estimation of population moments and parameters in biased sampling. Stat (Int Stat Inst) 2020. [DOI: 10.1002/sta4.241] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Yuya Shimizu
- Graduate School of EconomicsKeio University Tokyo Japan
| | - Takahiro Hoshino
- Faculty of EconomicsKeio University Tokyo Japan
- RIKEN AIP Tokyo Japan
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21
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Fang X, Fang B, Wang C, Xia T, Bottai M, Fang F, Cao Y. Comparison of Frequentist and Bayesian Generalized Additive Models for Assessing the Association Between Daily Exposure to Fine Particles and Respiratory Mortality: A Simulation Study. INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2019; 16:ijerph16050746. [PMID: 30832258 PMCID: PMC6427163 DOI: 10.3390/ijerph16050746] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/01/2019] [Revised: 02/25/2019] [Accepted: 02/26/2019] [Indexed: 11/16/2022]
Abstract
Objective: To compare the performance of frequentist and Bayesian generalized additive models (GAMs) in terms of accuracy and precision for assessing the association between daily exposure to fine particles and respiratory mortality using simulated data based on a real time-series study. Methods: In our study, we examined the estimates from a fully Bayesian GAM using simulated data based on a genuine time-series study on fine particles with a diameter of 2.5 μm or less (PM2.5) and respiratory deaths conducted in Shanghai, China. The simulation was performed by multiplying the observed daily death with a random error. The underlying priors for Bayesian analysis are estimated using the real world time-series data. We also examined the sensitivity of Bayesian GAM to the choice of priors and to true parameter. Results: The frequentist GAM and Bayesian GAM show similar means and variances of the estimates of the parameters of interest. However, the estimates from Bayesian GAM show relatively more fluctuation, which to some extent reflects the uncertainty inherent in Bayesian estimation. Conclusions: Although computationally intensive, Bayesian GAM would be a better solution to avoid potentially over-confident inferences. With the increasing computing power of computers and statistical packages available, fully Bayesian methods for decision making may become more widely applied in the future.
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Affiliation(s)
- Xin Fang
- Unit of Biostatistics, Institute of Environmental Medicine, Karolinska Institutet, 17177 Stockholm, Sweden.
| | - Bo Fang
- Division of Vital Statistics, Shanghai Municipal Center for Disease Control and Prevention, Shanghai 200336, China.
| | - Chunfang Wang
- Division of Vital Statistics, Shanghai Municipal Center for Disease Control and Prevention, Shanghai 200336, China.
| | - Tian Xia
- Institute of Health Information, Shanghai Municipal Center for Disease Control and Prevention, Shanghai 200336, China.
| | - Matteo Bottai
- Unit of Biostatistics, Institute of Environmental Medicine, Karolinska Institutet, 17177 Stockholm, Sweden.
| | - Fang Fang
- Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, 17177 Stockholm, Sweden.
| | - Yang Cao
- Clinical Epidemiology and Biostatistics, School of Medical Sciences, Örebro University, 70182 Örebro, Sweden.
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22
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Reda Abonazel M, Gad AAE. Robust partial residuals estimation in semiparametric partially linear model. COMMUN STAT-SIMUL C 2018. [DOI: 10.1080/03610918.2018.1494279] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Mohamed Reda Abonazel
- Department of Applied Statistics and Econometrics, Institute of Statistical Studies and Research, Cairo University, Giza, Egypt
| | - Ahmed Abd-Elfatah Gad
- Department of Statistics and Insurance, Faculty of Commerce, Zagazig University, Zagazig, Egypt
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23
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Zhang J, Zhou Y, Cui X, Xu W. Semiparametric quantile estimation for varying coefficient partially linear measurement errors models. BRAZ J PROBAB STAT 2018. [DOI: 10.1214/17-bjps357] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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24
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Zhang J, Zhou N, Chen Q, Chu T. Nonlinear measurement errors models subject to partial linear additive distortion. BRAZ J PROBAB STAT 2018. [DOI: 10.1214/16-bjps333] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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25
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Afzal AR, Dong C, Lu X. Estimation of partly linear additive hazards model with left-truncated and right-censored data. STAT MODEL 2017. [DOI: 10.1177/1471082x17705993] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
In this article, we consider an additive hazards semiparametric model for left-truncated and right-censored data where the risk function has a partly linear structure, we call it the partly linear additive hazards model. The nonlinear components are assumed to be B-splines functions, so the model can be viewed as a semiparametric model with an unknown baseline hazard function and a partly linear parametric risk function, which can model both linear and nonlinear covariate effects, hence is more flexible than a purely linear or nonlinear model. We construct a pseudo-score function to estimate the coefficients of the linear covariates and the B-spline basis functions. The proposed estimators are asymptotically normal under the assumption that the true nonlinear functions are B-spline functions whose knot locations and number of knots are held fixed. On the other hand, when the risk functions are unknown non-parametric functions, the proposed method provides a practical solution to the underlying inference problems. We conduct simulation studies to empirically examine the finite-sample performance of the proposed method and analyze a real dataset for illustration.
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Affiliation(s)
- Arfan Raheen Afzal
- Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada
| | - Cheng Dong
- Department of Statistics University of Missouri, Columbia, MO, U.S.A
| | - Xuewen Lu
- Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada
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26
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Yang L, Fang Y, Wang J, Shao Y. Variable selection for partially linear models via learning gradients. Electron J Stat 2017. [DOI: 10.1214/17-ejs1300] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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27
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Sha Q, Zhang K, Zhang S. A Nonparametric Regression Approach to Control for Population Stratification in Rare Variant Association Studies. Sci Rep 2016; 6:37444. [PMID: 27857226 PMCID: PMC5114546 DOI: 10.1038/srep37444] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2016] [Accepted: 10/28/2016] [Indexed: 01/31/2023] Open
Abstract
Recently, there is increasing interest to detect associations between rare variants and complex traits. Rare variant association studies usually need large sample sizes due to the rarity of the variants, and large sample sizes typically require combining information from different geographic locations within and across countries. Although several statistical methods have been developed to control for population stratification in common variant association studies, these methods are not necessarily controlling for population stratification in rare variant association studies. Thus, new statistical methods that can control for population stratification in rare variant association studies are needed. In this article, we propose a principal component based nonparametric regression (PC-nonp) approach to control for population stratification in rare variant association studies. Our simulations show that the proposed PC-nonp can control for population stratification well in all scenarios, while existing methods cannot control for population stratification at least in some scenarios. Simulations also show that PC-nonp's robustness to population stratification will not reduce power. Furthermore, we illustrate our proposed method by using whole genome sequencing data from genetic analysis workshop 18 (GAW18).
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Affiliation(s)
- Qiuying Sha
- Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA
| | - Kui Zhang
- Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA
| | - Shuanglin Zhang
- Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA
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28
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Affiliation(s)
| | - Xiang‐Nan Feng
- Department of Statistics The Chinese University of Hong Kong
| | - Min Chen
- Academy of Mathematics System Science Chinese Academy of Sciences
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Tang Y, Sinha D, Pati D, Lipsitz S, Lipshultz S. Bayesian partial linear model for skewed longitudinal data. Biostatistics 2015; 16:441-53. [PMID: 25792623 DOI: 10.1093/biostatistics/kxv005] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2014] [Accepted: 02/12/2015] [Indexed: 11/13/2022] Open
Abstract
Unlike majority of current statistical models and methods focusing on mean response for highly skewed longitudinal data, we present a novel model for such data accommodating a partially linear median regression function, a skewed error distribution and within subject association structures. We provide theoretical justifications for our methods including asymptotic properties of the posterior and associated semiparametric Bayesian estimators. We also provide simulation studies to investigate the finite sample properties of our methods. Several advantages of our method compared with existing methods are demonstrated via analysis of a cardiotoxicity study of children of HIV-infected mothers.
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Affiliation(s)
- Yuanyuan Tang
- Department of Statistics, Florida State University, Tallahassee, FL, USA
| | - Debajyoti Sinha
- Department of Statistics, Florida State University, Tallahassee, FL, USA
| | - Debdeep Pati
- Department of Statistics, Florida State University, Tallahassee, FL, USA
| | | | - Steven Lipshultz
- Department of Pediatrics, Wayne State University School of Medicine and Children's Hospital of Michigan, Detroit, MI, USA
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Cheng G, Zhou L, Huang JZ. Efficient semiparametric estimation in generalized partially linear additive models for longitudinal/clustered data. BERNOULLI 2014. [DOI: 10.3150/12-bej479] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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31
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Henry G, Rodriguez D. Robust estimators in partly linear regression models on Riemannian manifolds. COMMUN STAT-THEOR M 2014. [DOI: 10.1080/03610926.2013.775302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Guillermo Henry
- a Facultad de Ciencias Exactas y Naturales , Universidad de Buenos Aires and CONICET , Argentina
| | - Daniela Rodriguez
- a Facultad de Ciencias Exactas y Naturales , Universidad de Buenos Aires and CONICET , Argentina
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Abstract
Methodology for regression beyond the mean has been a goal of researchers for many years. This discussion provides some additional context for the important ideas in the present paper, by recounting some of the historical background to the GAMLSS approach and pointing to the power and appeal of fully probabilistic regression analysis in the setting of Bayesian nonparametrics.
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Affiliation(s)
- Peter J Green
- University of Bristol and University of Technology, Sydney, Australia
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35
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Zhang JJ, Liang HY. Asymptotic Normality of Estimators in Heteroscedastic Semi-Parametric Model with Strong Mixing Errors. COMMUN STAT-THEOR M 2012. [DOI: 10.1080/03610926.2011.558663] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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36
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Zhang J, Wang T, Zhu L, Liang H. A dimension reduction based approach for estimation and variable selection in partially linear single-index models with high-dimensional covariates. Electron J Stat 2012. [DOI: 10.1214/12-ejs744] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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37
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Yu K, Mammen E, Park BU. Semi-parametric regression: Efficiency gains from modeling the nonparametric part. BERNOULLI 2011. [DOI: 10.3150/10-bej296] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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38
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Wang L, Brown LD, Cai TT. A difference based approach to the semiparametric partial linear model. Electron J Stat 2011. [DOI: 10.1214/11-ejs621] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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39
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Liang H, Liu X, Li R, Tsai CL. ESTIMATION AND TESTING FOR PARTIALLY LINEAR SINGLE-INDEX MODELS. Ann Stat 2010; 38:3811-3836. [PMID: 21625330 PMCID: PMC3102543 DOI: 10.1214/10-aos835] [Citation(s) in RCA: 134] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
In partially linear single-index models, we obtain the semiparametrically efficient profile least-squares estimators of regression coefficients. We also employ the smoothly clipped absolute deviation penalty (SCAD) approach to simultaneously select variables and estimate regression coefficients. We show that the resulting SCAD estimators are consistent and possess the oracle property. Subsequently, we demonstrate that a proposed tuning parameter selector, BIC, identifies the true model consistently. Finally, we develop a linear hypothesis test for the parametric coefficients and a goodness-of-fit test for the nonparametric component, respectively. Monte Carlo studies are also presented.
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Affiliation(s)
- Hua Liang
- Department of Biostatistics and Computational Biology, University of Rochester, Rochester, New York 14642, USA, ,
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41
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Paciorek CJ. The importance of scale for spatial-confounding bias and precision of spatial regression estimators. Stat Sci 2010; 25:107-125. [PMID: 21528104 DOI: 10.1214/10-sts326] [Citation(s) in RCA: 120] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
Residuals in regression models are often spatially correlated. Prominent examples include studies in environmental epidemiology to understand the chronic health effects of pollutants. I consider the effects of residual spatial structure on the bias and precision of regression coefficients, developing a simple framework in which to understand the key issues and derive informative analytic results. When unmeasured confounding introduces spatial structure into the residuals, regression models with spatial random effects and closely-related models such as kriging and penalized splines are biased, even when the residual variance components are known. Analytic and simulation results show how the bias depends on the spatial scales of the covariate and the residual: one can reduce bias by fitting a spatial model only when there is variation in the covariate at a scale smaller than the scale of the unmeasured confounding. I also discuss how the scales of the residual and the covariate affect efficiency and uncertainty estimation when the residuals are independent of the covariate. In an application on the association between black carbon particulate matter air pollution and birth weight, controlling for large-scale spatial variation appears to reduce bias from unmeasured confounders, while increasing uncertainty in the estimated pollution effect.
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Affiliation(s)
- Christopher J Paciorek
- Department of Biostatistics, Harvard School of Public Health, 655 Huntington Avenue, Boston, Massachusetts 02115; Department of Statistics, 367 Evans Hall, University of California, Berkeley, California 94720, url: www.biostat.harvard.edu/~paciorek
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42
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43
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Zhou Y, Liang H. Statistical Inference for Semiparametric Varying-coefficient Partially Linear Models with Generated Regressors (F06-463). Ann Stat 2009; 37:427-458. [PMID: 20126281 DOI: 10.1214/07-aos561] [Citation(s) in RCA: 89] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
We study semiparametric varying-coefficient partially linear models when some linear covariates are not observed, but ancillary variables are available. Semiparametric profile least-square-based estimation procedures are developed for parametric and nonparametric components after we calibrate the error-prone covariates. Asymptotic properties of the proposed estimators are established. We also propose the profile least-square-based ratio test and Wald test to identify significant parametric and nonparametric components. To improve accuracy of the proposed tests for small or moderate sample sizes, Wild bootstrap version is also proposed to calculate the critical values. Intensive simulation experiments are conducted to illustrate the proposed approaches.
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Affiliation(s)
- Yong Zhou
- Institute of Applied Mathematics, Academy of Mathematics and System Science,Chinese Academy of Science, Beijing, China, 100080
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Abstract
Semiparametric regression is a fusion between parametric regression and nonparametric regression that integrates low-rank penalized splines, mixed model and hierarchical Bayesian methodology - thus allowing more streamlined handling of longitudinal and spatial correlation. We review progress in the field over the five-year period between 2003 and 2007. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application.
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Affiliation(s)
- David Ruppert
- School of Operations Research and Information Engineering, Cornell University, 1170 Comstock Hall, Ithaca, NY 14853, U.S.A
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45
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Antoniadis A. Wavelet methods in statistics: some recent developments and their applications. STATISTICS SURVEYS 2007. [DOI: 10.1214/07-ss014] [Citation(s) in RCA: 94] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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46
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Ahmad I, Leelahanon S, Li Q. Efficient estimation of a semiparametric partially linear varying coefficient model. Ann Stat 2005. [DOI: 10.1214/009053604000000931] [Citation(s) in RCA: 128] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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47
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Bunea F. Consistent covariate selection and post model selection inference in semiparametric regression. Ann Stat 2004. [DOI: 10.1214/009053604000000247] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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48
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Aneiros-Pérez G, González-Manteiga W, Vieu P. Estimation and testing in a partial linear regression model
under long-memory dependence. BERNOULLI 2004. [DOI: 10.3150/bj/1077544603] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
| | | | - Philippe Vieu
- Laboratoire de Statistique et Probabilités, UMR CNRS C55830
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49
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Liang H, H^|^auml;rdle W. 3. Statistical Models for Biomedical Research. JOURNAL JAPANESE SOCIETY OF COMPUTATIONAL STATISTICS 2003. [DOI: 10.5183/jjscs1988.15.2_89] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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50
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Delgado MA, Manteiga WG. Significance testing in nonparametric regression based on the bootstrap. Ann Stat 2001. [DOI: 10.1214/aos/1013203462] [Citation(s) in RCA: 85] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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