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Yang X, Chen J, Li D, Li R. Functional-Coefficient Quantile Regression for Panel Data with Latent Group Structure. JOURNAL OF BUSINESS & ECONOMIC STATISTICS : A PUBLICATION OF THE AMERICAN STATISTICAL ASSOCIATION 2023; 42:1026-1040. [PMID: 39022132 PMCID: PMC11250162 DOI: 10.1080/07350015.2023.2277172] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/20/2024]
Abstract
This paper considers estimating functional-coefficient models in panel quantile regression with individual effects, allowing the cross-sectional and temporal dependence for large panel observations. A latent group structure is imposed on the heterogenous quantile regression models so that the number of nonparametric functional coefficients to be estimated can be reduced considerably. With the preliminary local linear quantile estimates of the subject-specific functional coefficients, a classic agglomerative clustering algorithm is used to estimate the unknown group structure and an easy-to-implement ratio criterion is proposed to determine the group number. The estimated group number and structure are shown to be consistent. Furthermore, a post-grouping local linear smoothing method is introduced to estimate the group-specific functional coefficients, and the relevant asymptotic normal distribution theory is derived with a normalisation rate comparable to that in the literature. The developed methodologies and theory are verified through a simulation study and showcased with an application to house price data from UK local authority districts, which reveals different homogeneity structures at different quantile levels.
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Affiliation(s)
- Xiaorong Yang
- School of Statistics and Mathematics,Zhejiang Gongshang University
| | - Jia Chen
- Department of Economics and Related Studies, University of York
| | - Degui Li
- Department of Mathematics, University of York
| | - Runze Li
- Department of Statistics, Pennsylvania State University
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2
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Kai B, Huang M, Yao W, Dong Y. Nonparametric and Semiparametric Quantile Regression via a New MM Algorithm. J Comput Graph Stat 2023. [DOI: 10.1080/10618600.2023.2184374] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/25/2023]
Affiliation(s)
- Bo Kai
- Department of Mathematics, College of Charleston
| | - Mian Huang
- School of Statistics and Management, Shanghai University of Finance and Economics
| | - Weixin Yao
- Department of Statistics, University of California, Riverside
| | - Yuexiao Dong
- Department of Statistics, Operations, and Data Science, Temple University
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3
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Hlubinka D, Kotík L, Šiman M. Multivariate Quantiles with Both Overall and Directional Probability Interpretation. Scand Stat Theory Appl 2022. [DOI: 10.1111/sjos.12603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Daniel Hlubinka
- Univerzita Karlova Matematicko‐fyzikální fakulta, Department of Probability and Statistics
| | | | - Miroslav Šiman
- Institute of Information Theory and Automation Czech Academy of Sciences
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Zheng Y, Zhao X, Zhang X. Quantile regression for massive data with network-induced dependence, and application to the New York statewide planning and research cooperative system. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2020.1786120] [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)
- Yanqiao Zheng
- Department of Financial Engineering, School of Finance, Zhejiang University of Finance and Economics, Hangzhou, China
| | - Xiaobing Zhao
- School of Data Sciences, Zhejiang University of Finance and Economics, Hangzhou, China
| | - Xiaoqi Zhang
- Department of Financial Engineering, School of Finance, Zhejiang University of Finance and Economics, Hangzhou, China
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Liu CS, Liang HY. Bayesian analysis in single-index quantile regression with missing observation. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2022.2042027] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Chang-Sheng Liu
- School of Mathematical Sciences, Tongji University, Shanghai, China
| | - Han-Ying Liang
- School of Mathematical Sciences, Tongji University, Shanghai, China
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Feng H, Luo Q. A weighted quantile regression for nonlinear models with randomly censored data. COMMUN STAT-THEOR M 2021. [DOI: 10.1080/03610926.2020.1713364] [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)
- Hailin Feng
- School of Mathematics and Statistics, Xidian University, Xian, China
| | - Qianqian Luo
- School of Mathematics and Statistics, Xidian University, Xian, China
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7
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Bayesian Analysis of Partially Linear Additive Spatial Autoregressive Models with Free-Knot Splines. Symmetry (Basel) 2021. [DOI: 10.3390/sym13091635] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
This article deals with symmetrical data that can be modelled based on Gaussian distribution. We consider a class of partially linear additive spatial autoregressive (PLASAR) models for spatial data. We develop a Bayesian free-knot splines approach to approximate the nonparametric functions. It can be performed to facilitate efficient Markov chain Monte Carlo (MCMC) tools to design a Gibbs sampler to explore the full conditional posterior distributions and analyze the PLASAR models. In order to acquire a rapidly-convergent algorithm, a modified Bayesian free-knot splines approach incorporated with powerful MCMC techniques is employed. The Bayesian estimator (BE) method is more computationally efficient than the generalized method of moments estimator (GMME) and thus capable of handling large scales of spatial data. The performance of the PLASAR model and methodology is illustrated by a simulation, and the model is used to analyze a Sydney real estate dataset.
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Liang HY, Wang BH, Shen Y. Quantile regression of partially linear single-index model with missing observations. STATISTICS-ABINGDON 2021. [DOI: 10.1080/02331888.2021.1883613] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Han-Ying Liang
- School of Mathematical Sciences, Tongji University, Shanghai, People's Republic of China
| | - Bao-Hua Wang
- School of Mathematical Sciences, Tongji University, Shanghai, People's Republic of China
| | - Yu Shen
- School of Mathematical Sciences, Tongji University, Shanghai, People's Republic of China
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Li R, Zhang Y. Two-stage estimation and simultaneous confidence band in partially nonlinear additive model. METRIKA 2021. [DOI: 10.1007/s00184-021-00808-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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10
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Bai Y, Tian M, Tang ML, Lee WY. Variable selection for ultra-high dimensional quantile regression with missing data and measurement error. Stat Methods Med Res 2020; 30:129-150. [PMID: 32746735 DOI: 10.1177/0962280220941533] [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: 11/15/2022]
Abstract
In this paper, we consider variable selection for ultra-high dimensional quantile regression model with missing data and measurement errors in covariates. Specifically, we correct the bias in the loss function caused by measurement error by applying the orthogonal quantile regression approach and remove the bias caused by missing data using the inverse probability weighting. A nonconvex Atan penalized estimation method is proposed for simultaneous variable selection and estimation. With the proper choice of the regularization parameter and under some relaxed conditions, we show that the proposed estimate enjoys the oracle properties. The choice of smoothing parameters is also discussed. The performance of the proposed variable selection procedure is assessed by Monte Carlo simulation studies. We further demonstrate the proposed procedure with a breast cancer data set.
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Affiliation(s)
- Yongxin Bai
- Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing, China
| | - Maozai Tian
- Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing, China.,School of Statistics and Information, Xinjiang University of Finance and Economics, Urumqi, China.,School of Statistics, Lanzhou University of Finance and Economics, Lanzhou, China
| | - Man-Lai Tang
- Department of Mathematics, Statistics and Insurance, The Hang Seng University of Hong Kong, Siu Lek Yuen, China.,Big Data Intelligence Centre, The Hang Seng University of Hong Kong, Siu Lek Yuen, China
| | - Wing-Yan Lee
- Department of Mathematics, Statistics and Insurance, The Hang Seng University of Hong Kong, Siu Lek Yuen, China
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Affiliation(s)
- Pavel Čížek
- Department of Econometrics & Operations Research Tilburg University Tilburg The Netherlands
| | - Serhan Sadıkoğlu
- Department of Econometrics & Operations Research Tilburg University Tilburg The Netherlands
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12
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A plug-in bandwidth selector for nonparametric quantile regression. TEST-SPAIN 2019. [DOI: 10.1007/s11749-018-0582-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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13
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Zhao X, Wang W, Liu L, Shih YCT. A flexible quantile regression model for medical costs with application to Medical Expenditure Panel Survey Study. Stat Med 2018; 37:2645-2666. [PMID: 29722044 DOI: 10.1002/sim.7670] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2016] [Revised: 03/03/2018] [Accepted: 03/08/2018] [Indexed: 11/11/2022]
Abstract
Medical costs are often skewed to the right and heteroscedastic, having a sophisticated relation with covariates. Mean function regression models with low-dimensional covariates have been extensively considered in the literature. However, it is important to develop a robust alternative to find the underlying relationship between medical costs and high-dimensional covariates. In this paper, we propose a new quantile regression model to analyze medical costs. We also consider variable selection, using an adaptive lasso penalized variable selection method to identify significant factors of the covariates. Simulation studies are conducted to illustrate the performance of the estimation method. We apply our method to the analysis of the Medical Expenditure Panel Survey dataset.
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Affiliation(s)
- Xiaobing Zhao
- School of Data Sciences, Zhejiang University of Finance and Economics, Hangzhou, Zhejiang, China
| | - Weiwei Wang
- School of Statistics, East China Normal University, Shanghai, China
| | - Lei Liu
- Division of Biostatistics, Washington University in St. Louis, St. Louis, MO, U.S.A
| | - Ya-Chen T Shih
- Department of Health Services Research, MD Anderson Cancer Center, Houston, TX, U.S.A
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Abstract
We investigate a new kernel-weighted likelihood smoothing quantile regression method. The likelihood is based on a normal scale-mixture representation of asymmetric Laplace distribution (ALD). This approach enjoys the same good design adaptation as the local quantile regression ( Spokoiny et al., 2013 , Journal of Statistical Planning and Inference, 143, 1109–1129), particularly for smoothing extreme quantile curves, and ensures non-crossing quantile curves for any given sample. The performance of the proposed method is evaluated via extensive Monte Carlo simulation studies and one real data analysis.
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Affiliation(s)
- Xi Liu
- School of Management, Hefei University of Technology, Hefei, Anhui, China
- Department of Mathematics, Brunel University London, London, UK
| | - Keming Yu
- Department of Mathematics, Brunel University London, London, UK
| | - Qifa Xu
- School of Management, Hefei University of Technology, Hefei, Anhui, China
| | - Xueqing Tang
- School of Science, Jiangnan University, Wuxi, Jiangsu, China
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Yang J, Lu F, Yang H. Quantile regression for robust inference on varying coefficient partially nonlinear models. J Korean Stat Soc 2018. [DOI: 10.1016/j.jkss.2017.12.002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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16
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Zhang Y, Lian H, Yu Y. Estimation and variable selection for quantile partially linear single-index models. J MULTIVARIATE ANAL 2017. [DOI: 10.1016/j.jmva.2017.09.006] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Hallin M, Lu Z, Paindaveine D, Šiman M. Local bilinear multiple-output quantile/depth regression. BERNOULLI 2015. [DOI: 10.3150/14-bej610] [Citation(s) in RCA: 13] [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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23
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Gu L, Yang L. Oracally efficient estimation for single-index link function with simultaneous confidence band. Electron J Stat 2015. [DOI: 10.1214/15-ejs1051] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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25
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Wu C, Yu Y. Partially linear modeling of conditional quantiles using penalized splines. Comput Stat Data Anal 2014. [DOI: 10.1016/j.csda.2014.02.020] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Sun J, Liao H, Upadhyaya BR. A robust functional-data-analysis method for data recovery in multichannel sensor systems. IEEE TRANSACTIONS ON CYBERNETICS 2014; 44:1420-1431. [PMID: 25051452 DOI: 10.1109/tcyb.2013.2285876] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Multichannel sensor systems are widely used in condition monitoring for effective failure prevention of critical equipment or processes. However, loss of sensor readings due to malfunctions of sensors and/or communication has long been a hurdle to reliable operations of such integrated systems. Moreover, asynchronous data sampling and/or limited data transmission are usually seen in multiple sensor channels. To reliably perform fault diagnosis and prognosis in such operating environments, a data recovery method based on functional principal component analysis (FPCA) can be utilized. However, traditional FPCA methods are not robust to outliers and their capabilities are limited in recovering signals with strongly skewed distributions (i.e., lack of symmetry). This paper provides a robust data-recovery method based on functional data analysis to enhance the reliability of multichannel sensor systems. The method not only considers the possibly skewed distribution of each channel of signal trajectories, but is also capable of recovering missing data for both individual and correlated sensor channels with asynchronous data that may be sparse as well. In particular, grand median functions, rather than classical grand mean functions, are utilized for robust smoothing of sensor signals. Furthermore, the relationship between the functional scores of two correlated signals is modeled using multivariate functional regression to enhance the overall data-recovery capability. An experimental flow-control loop that mimics the operation of coolant-flow loop in a multimodular integral pressurized water reactor is used to demonstrate the effectiveness and adaptability of the proposed data-recovery method. The computational results illustrate that the proposed method is robust to outliers and more capable than the existing FPCA-based method in terms of the accuracy in recovering strongly skewed signals. In addition, turbofan engine data are also analyzed to verify the capability of the proposed method in recovering non-skewed signals.
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28
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Testing for additivity in nonparametric quantile regression. ANN I STAT MATH 2014. [DOI: 10.1007/s10463-014-0461-1] [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]
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29
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Comments on: An updated review of Goodness-of-Fit tests for regression models. TEST-SPAIN 2013. [DOI: 10.1007/s11749-013-0333-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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31
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Lu Y. Estimation for the Power-transformed Varying-coefficient Quantile Regression Model. COMMUN STAT-THEOR M 2013. [DOI: 10.1080/03610926.2011.615436] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Lee YK, Mammen E, Park BU. Backfitting and smooth backfitting for additive quantile models. Ann Stat 2010. [DOI: 10.1214/10-aos808] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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CHENG YEBIN, DE GOOIJER JANG, ZEROM DAWIT. Efficient Estimation of an Additive Quantile Regression Model. Scand Stat Theory Appl 2010. [DOI: 10.1111/j.1467-9469.2010.00706.x] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Cai Z, Xu X. Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models. J Am Stat Assoc 2009. [DOI: 10.1198/jasa.2009.0102] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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41
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Similä T. Self-organizing map visualizing conditional quantile functions with multidimensional covariates. Comput Stat Data Anal 2006. [DOI: 10.1016/j.csda.2005.03.001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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