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Yu W, Bondell HD. Variational Bayes for fast and accurate empirical likelihood inference. J Am Stat Assoc 2023. [DOI: 10.1080/01621459.2023.2169701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Weichang Yu
- School of Mathematics and Statistics, The University of Melbourne
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2
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Moon C, Bedoui A. Bayesian elastic net based on empirical likelihood. J STAT COMPUT SIM 2022. [DOI: 10.1080/00949655.2022.2148254] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Affiliation(s)
- Chul Moon
- Department of Statistical Science, Southern Methodist University, Dallas, TX, USA
| | - Adel Bedoui
- Department of Statistics, University of Georgia, Athens, GA, USA
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3
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Jahan F, Kennedy DW, Duncan EW, Mengersen KL. Evaluation of spatial Bayesian Empirical Likelihood models in analysis of small area data. PLoS One 2022; 17:e0268130. [PMID: 35622835 PMCID: PMC9140259 DOI: 10.1371/journal.pone.0268130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2021] [Accepted: 04/24/2022] [Indexed: 12/01/2022] Open
Abstract
Bayesian empirical likelihood (BEL) models are becoming increasingly popular as an attractive alternative to fully parametric models. However, they have only recently been applied to spatial data analysis for small area estimation. This study considers the development of spatial BEL models using two popular conditional autoregressive (CAR) priors, namely BYM and Leroux priors. The performance of the proposed models is compared with their parametric counterparts and with existing spatial BEL models using independent Gaussian priors and generalised Moran basis priors. The models are applied to two benchmark spatial datasets, simulation study and COVID-19 data. The results indicate promising opportunities for these models to capture new insights into spatial data. Specifically, the spatial BEL models outperform the parametric spatial models when the underlying distributional assumptions of data appear to be violated.
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Affiliation(s)
- Farzana Jahan
- School of Mathematical Sciences, ARC Centre of Excellence in Mathematical and Statistical Frontiers (ACEMS), QUT Centre for Data Science, Faculty of Science, Queensland University of Technology, Brisbane, Queensland, Australia
- * E-mail:
| | - Daniel W. Kennedy
- School of Mathematical Sciences, ARC Centre of Excellence in Mathematical and Statistical Frontiers (ACEMS), QUT Centre for Data Science, Faculty of Science, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Earl W. Duncan
- School of Mathematical Sciences, ARC Centre of Excellence in Mathematical and Statistical Frontiers (ACEMS), QUT Centre for Data Science, Faculty of Science, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Kerrie L. Mengersen
- School of Mathematical Sciences, ARC Centre of Excellence in Mathematical and Statistical Frontiers (ACEMS), QUT Centre for Data Science, Faculty of Science, Queensland University of Technology, Brisbane, Queensland, Australia
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4
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Liu B, Zhao H, Wang C. Bayesian empirical likelihood of linear regression model with current status data. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2022.2044491] [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)
- Binxia Liu
- College of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, P.R. China
| | - Hui Zhao
- College of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, P.R. China
| | - Chunjie Wang
- College of Mathematics and Statistics, Changchun University of Technology, Changchun, P.R. China
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5
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Lin R, Chan KG, Shi H. A unified Bayesian framework for exact inference of area under the receiver operating characteristic curve. Stat Methods Med Res 2021; 30:2269-2287. [PMID: 34468238 DOI: 10.1177/09622802211037070] [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
The area under the receiver operating characteristic curve is a widely used measure for evaluating the performance of a diagnostic test. Common approaches for inference on area under the receiver operating characteristic curve are usually based upon approximation. For example, the normal approximation based inference tends to suffer from the problem of low accuracy for small sample size. Frequentist empirical likelihood based approaches for area under the receiver operating characteristic curve estimation may perform better, but are usually conducted through approximation in order to reduce the computational burden, thus the inference is not exact. By contrast, we proposed an exact inferential procedure by adapting the empirical likelihood into a Bayesian framework and draw inference from the posterior samples of the area under the receiver operating characteristic curve obtained via a Gibbs sampler. The full conditional distributions within the Gibbs sampler only involve empirical likelihoods with linear constraints, which greatly simplify the computation. To further enhance the applicability and flexibility of the Bayesian empirical likelihood, we extend our method to the estimation of partial area under the receiver operating characteristic curve, comparison of multiple tests, and the doubly robust estimation of area under the receiver operating characteristic curve in the presence of missing test results. Simulation studies confirm the desirable performance of the proposed methods, and a real application is presented to illustrate its usefulness.
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Affiliation(s)
- Ruitao Lin
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, USA
| | - Kc Gary Chan
- Department of Biostatistics, 7284University of Washington, USA
| | - Haolun Shi
- Department of Statistics and Actuarial Science, Simon Fraser University, Canada
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Jiang Z, Yang B, Qin J, Zhou Y. Enhanced empirical likelihood estimation of incubation period of COVID-19 by integrating published information. Stat Med 2021; 40:4252-4268. [PMID: 33973260 PMCID: PMC8242591 DOI: 10.1002/sim.9026] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Revised: 04/21/2021] [Accepted: 04/23/2021] [Indexed: 12/05/2022]
Abstract
Since the outbreak of the new coronavirus disease (COVID‐19), a large number of scientific studies and data analysis reports have been published in the International Journal of Medicine and Statistics. Taking the estimation of the incubation period as an example, we propose a low‐cost method to integrate external research results and available internal data together. By using empirical likelihood method, we can effectively incorporate summarized information even if it may be derived from a misspecified model. Taking the possible uncertainty in summarized information into account, we augment a logarithm of the normal density in the log empirical likelihood. We show that the augmented log‐empirical likelihood can produce enhanced estimates for the underlying parameters compared with the method without utilizing auxiliary information. Moreover, the Wilks' theorem is proved to be true. We illustrate our methodology by analyzing a COVID‐19 incubation period data set retrieved from Zhejiang Province and summarized information from a similar study in Shenzhen, China.
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Affiliation(s)
- Zhongfeng Jiang
- Academy of Mathematics and System SciencesChinese Academy of ScienceBeijingChina
| | - Baoying Yang
- Department of Statistics, College of MathematicsSouthwest Jiaotong UniversityChengduChina
| | - Jing Qin
- National Institute of Allergy and Infectious DiseasesNational Institute of HealthBethesdaMarylandUSA
| | - Yong Zhou
- Key Laboratory of Advanced Theory and Application in Statistics and Data ScienceMOEShanghaiChina
- Academy of Statistics and Interdisciplinary SciencesEast China Normal UniversityShanghaiChina
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8
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Huang CY, Qin J. A unified approach for synthesizing population-level covariate effect information in semiparametric estimation with survival data. Stat Med 2020; 39:1573-1590. [PMID: 32073677 DOI: 10.1002/sim.8499] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2018] [Revised: 08/22/2019] [Accepted: 10/28/2019] [Indexed: 01/12/2023]
Abstract
There has been a growing interest in developing methodologies to combine information from public domains to improve efficiency in the analysis of relatively small-scale studies that collect more detailed patient-level information. The auxiliary information is usually given in the form of summary statistics or regression coefficients. Thus, the question arises as to how to incorporate the summary information in the model estimation procedure. In this article, we consider statistical analysis of right-censored survival data when additional information about the covariate effects evaluated in a reduced Cox model is available. Recognizing that such external information can be summarized using population moments, we present a unified framework by employing the generalized method of moments to combine information from different sources for the analysis of survival data. The proposed estimator can be shown to be consistent and asymptotically normal; moreover, it is more efficient than the maximum partial likelihood estimator. We also consider incorporating uncertainty of the external information in the inference procedure. Simulation studies show that, by incorporating the additional summary information, the proposed estimators enjoy a substantial gain in efficiency over the conventional approach. A data analysis of a pancreatic cancer cohort study is presented to illustrate the methods and theory.
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Affiliation(s)
- Chiung-Yu Huang
- Department of Epidemiology and Biostatistics, University of California at San Francisco, San Francisco, California
| | - Jing Qin
- Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, Maryland
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9
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Zhao P, Ghosh M, Rao JNK, Wu C. Bayesian empirical likelihood inference with complex survey data. J R Stat Soc Series B Stat Methodol 2019. [DOI: 10.1111/rssb.12342] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Puying Zhao
- Yunnan University; Kunming People's Republic of China
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Wang X, Wang D, Yang K, Xu D. Estimation and testing for the integer-valued threshold autoregressive models based on negative binomial thinning. COMMUN STAT-SIMUL C 2019. [DOI: 10.1080/03610918.2019.1586929] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Xiaohong Wang
- School of Mathematics, Jilin University, Changchun, Jilin, China
- College of Mathematics, Jilin Normal University, Siping, Jilin, China
| | - Dehui Wang
- School of Mathematics, Jilin University, Changchun, Jilin, China
| | - Kai Yang
- School of Mathematics and Statistics, Changchun University of Technology, Changchun, Jilin, China
| | - Da Xu
- School of Mathematics, Jilin University, Changchun, Jilin, China
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11
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Affiliation(s)
- Siddhartha Chib
- Olin Business School, Washington University in St. Louis, St. Louis, MO
| | - Minchul Shin
- Department of Economics, University of Illinois, Urbana, IL
| | - Anna Simoni
- CNRS - CREST, ENSAE, École Polytechnique, 5, Palaiseau, France
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12
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Wang YS, Drton M. Empirical likelihood for linear structural equation models with dependent errors. Stat (Int Stat Inst) 2017. [DOI: 10.1002/sta4.169] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Y. Samuel Wang
- Department of Statistics; University of Washington; Seattle 98103 WA USA
| | - Mathias Drton
- Department of Statistics; University of Washington; Seattle 98103 WA USA
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