{"title":"Empirical likelihood based Bayesian variable selection","authors":"Yichen Cheng , Yichuan Zhao","doi":"10.1016/j.csda.2025.108258","DOIUrl":null,"url":null,"abstract":"<div><div>Empirical likelihood is a popular nonparametric statistical tool that does not require any distributional assumptions. The possibility of conducting variable selection via Bayesian empirical likelihood is studied both theoretically and empirically. Theoretically, it is shown that when the prior distribution satisfies certain mild conditions, the corresponding Bayesian empirical likelihood estimators are posteriorly consistent and variable selection consistent. As special cases, the prior of Bayesian empirical likelihood LASSO and SCAD satisfy such conditions and thus can identify the non-zero elements of the parameters with probability approaching 1. In addition, it is easy to verify that those conditions are met for other widely used priors such as ridge, elastic net and adaptive LASSO. Empirical likelihood depends on a parameter that needs to be obtained by numerically solving a non-linear equation. Thus, there exists no conjugate prior for the posterior distribution, which causes the slow convergence of the MCMC sampling algorithm in some cases. To solve this problem, an approximation distribution is used as the proposal to enhance the acceptance rate and, therefore, facilitate faster computation. The computational results demonstrate quick convergence for the examples used in the paper. Both simulations and real data analyses are performed to illustrate the advantages of the proposed methods.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"213 ","pages":"Article 108258"},"PeriodicalIF":1.6000,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Statistics & Data Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167947325001343","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
Empirical likelihood is a popular nonparametric statistical tool that does not require any distributional assumptions. The possibility of conducting variable selection via Bayesian empirical likelihood is studied both theoretically and empirically. Theoretically, it is shown that when the prior distribution satisfies certain mild conditions, the corresponding Bayesian empirical likelihood estimators are posteriorly consistent and variable selection consistent. As special cases, the prior of Bayesian empirical likelihood LASSO and SCAD satisfy such conditions and thus can identify the non-zero elements of the parameters with probability approaching 1. In addition, it is easy to verify that those conditions are met for other widely used priors such as ridge, elastic net and adaptive LASSO. Empirical likelihood depends on a parameter that needs to be obtained by numerically solving a non-linear equation. Thus, there exists no conjugate prior for the posterior distribution, which causes the slow convergence of the MCMC sampling algorithm in some cases. To solve this problem, an approximation distribution is used as the proposal to enhance the acceptance rate and, therefore, facilitate faster computation. The computational results demonstrate quick convergence for the examples used in the paper. Both simulations and real data analyses are performed to illustrate the advantages of the proposed methods.
期刊介绍:
Computational Statistics and Data Analysis (CSDA), an Official Publication of the network Computational and Methodological Statistics (CMStatistics) and of the International Association for Statistical Computing (IASC), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. The journal consists of four refereed sections which are divided into the following subject areas:
I) Computational Statistics - Manuscripts dealing with: 1) the explicit impact of computers on statistical methodology (e.g., Bayesian computing, bioinformatics,computer graphics, computer intensive inferential methods, data exploration, data mining, expert systems, heuristics, knowledge based systems, machine learning, neural networks, numerical and optimization methods, parallel computing, statistical databases, statistical systems), and 2) the development, evaluation and validation of statistical software and algorithms. Software and algorithms can be submitted with manuscripts and will be stored together with the online article.
II) Statistical Methodology for Data Analysis - Manuscripts dealing with novel and original data analytical strategies and methodologies applied in biostatistics (design and analytic methods for clinical trials, epidemiological studies, statistical genetics, or genetic/environmental interactions), chemometrics, classification, data exploration, density estimation, design of experiments, environmetrics, education, image analysis, marketing, model free data exploration, pattern recognition, psychometrics, statistical physics, image processing, robust procedures.
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III) Special Applications - [...]
IV) Annals of Statistical Data Science [...]