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    188宝金博页面版: variable selection procedure from multiple testing

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    内容提示： SCIENCE CHINAMathematicshttps://doi.org/10.1007/s11425-016-9186-xc ? Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018 math.scichina.com link.springer.com. ARTICLES .Variable selection procedure from multiple testingBaoxue Zhang 1? , Guanghui Cheng 2 , Chunming Zhang 3 & Shurong Zheng 21 School of Statistics, Capital University of Economics and Business, Beijing 100070, China;2 School of Mathematics and Statistics and Key Laboratory of Applied Statistics of Ministry of Ed...

    文档格式：PDF | 页数：12 | 浏览次数：13 | 上传日期：2020-03-09 22:44:34 | 文档星级：
    SCIENCE CHINAMathematicshttps://doi.org/10.1007/s11425-016-9186-xc ? Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018 math.scichina.com link.springer.com. ARTICLES .Variable selection procedure from multiple testingBaoxue Zhang 1∗ , Guanghui Cheng 2 , Chunming Zhang 3 & Shurong Zheng 21 School of Statistics, Capital University of Economics and Business, Beijing 100070, China;2 School of Mathematics and Statistics and Key Laboratory of Applied Statistics of Ministry of Education,Northeast Normal University, Changchun 130024, China;3 Department of Statistics, University of Wisconsin-Madison, Madison, WI 53706, USAEmail: zhangbaoxue@cueb.edu.cn, chenggh845@nenu.edu.cn, cmzhang@stat.wisc.edu, zhengsr@nenu.edu.cnReceived December 7, 2016; accepted October 18, 2017Abstract Variable selection has played an important role in statistical learning and scientif i c discoveriesduring the past ten years, and multiple testing is a fundamental problem in statistical inference and also haswide application in many scientif i c f i elds. Signif i cant advances have been achieved in both areas. This studyattempts to f i nd a connection between adaptive LASSO (least absolute shrinkage and selection operator) andmultiple testing procedures in linear regression models. We also propose procedures based on multiple testingmethods to select variables and control the selection error rate, i.e., the false discovery rate. Simulation studiesdemonstrate that the proposed methods show good performance relative to controlling the selection error rateunder a wide range of settings.Keywords variable selection, multiple testing, adaptive LASSO, false discovery rate, linear regressionMSC(2010) 35J60, 35J70Citation: Zhang B X, Cheng G H, Zhang C M, et al. Variable selection procedure from multiple testing. SciChina Math, 2018, 61, https://doi.org/10.1007/s11425-016-9186-x1 IntroductionThe classical linear regression model is written as follows:Y = β 0 + X 1 β 1 + ··· + X p β p + ε, (1.1)where Y is the response variable, (X 1 ,...,X p ) are the potential explanatory variables, and ε is noise withmean zero and variance σ 2 . To increase prediction accuracy and facilitate model interpretation, manymethods have been developed to exclude insignif i cant predictors. Prior to 1990, traditional methods wereused for model selection, such as the Akaike information criterion, the Bayesian information criterion,and stepwise selection techniques. In 1996, Tibshirani [16] proposed LASSO, a simultaneous estimationand variable selection method that solves the l 1 -penalized regression problem of f i nding {β j } to minimizen∑i=1(y i − β 0 −∑jx ij β j) 2+ λp∑j=1|β j |,*Corresponding author

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