{"title":"Going beyond oracle property: Selection consistency and uniqueness of local solution of the generalized linear model","authors":"Chi Tim Ng , Seungyoung Oh , Youngjo Lee","doi":"10.1016/j.stamet.2016.05.006","DOIUrl":null,"url":null,"abstract":"<div><p><span><span>Recently, the selection consistency of penalized least square estimators<span> has received a great deal of attention. For the penalized likelihood estimation with certain non-convex penalties, search space can be constructed within which there exists a unique local minimizer that exhibits selection consistency in high-dimensional </span></span>generalized linear models under certain conditions. In particular, we prove that the SCAD penalty of Fan and Li (2001) and a new modified version of the unbounded penalty of Lee and Oh (2014) can be employed to achieve such a property. These results hold even for the non-sparse cases where the number of relevant </span>covariates increases with the sample size. Simulation studies are provided to compare the performance of SCAD penalty and the newly proposed penalty.</p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":"32 ","pages":"Pages 147-160"},"PeriodicalIF":0.0000,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2016.05.006","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Methodology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572312716300107","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 7
Abstract
Recently, the selection consistency of penalized least square estimators has received a great deal of attention. For the penalized likelihood estimation with certain non-convex penalties, search space can be constructed within which there exists a unique local minimizer that exhibits selection consistency in high-dimensional generalized linear models under certain conditions. In particular, we prove that the SCAD penalty of Fan and Li (2001) and a new modified version of the unbounded penalty of Lee and Oh (2014) can be employed to achieve such a property. These results hold even for the non-sparse cases where the number of relevant covariates increases with the sample size. Simulation studies are provided to compare the performance of SCAD penalty and the newly proposed penalty.
近年来，惩罚最小二乘估计的选择一致性问题受到了广泛的关注。对于具有一定非凸惩罚的惩罚似然估计，可以构造搜索空间，在该空间内存在唯一的局部最小值，且在一定条件下高维广义线性模型中表现出选择一致性。特别是，我们证明了可以使用Fan and Li(2001)的SCAD刑和Lee and Oh(2014)的无界刑的新修改版本来实现这一性质。这些结果甚至适用于相关协变量数量随样本量增加而增加的非稀疏情况。仿真研究比较了SCAD惩罚和新提出的惩罚的性能。
期刊介绍：
Statistical Methodology aims to publish articles of high quality reflecting the varied facets of contemporary statistical theory as well as of significant applications. In addition to helping to stimulate research, the journal intends to bring about interactions among statisticians and scientists in other disciplines broadly interested in statistical methodology. The journal focuses on traditional areas such as statistical inference, multivariate analysis, design of experiments, sampling theory, regression analysis, re-sampling methods, time series, nonparametric statistics, etc., and also gives special emphasis to established as well as emerging applied areas.
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