Robust and consistent variable selection in high-dimensional generalized linear models

被引：21

作者：

Avella-Medina, Marco ^{[1
]}

Ronchetti, Elvezio ^{[2
]}

机构：

[1] MIT, Sloan Sch Management, 30 Mem Dr, Cambridge, MA 02142 USA

[2] Univ Geneva, Res Ctr Stat, Blvd Pont Arve 40, CH-1205 Geneva, Switzerland

来源：

BIOMETRIKA | 2018年 / 105卷 / 01期

基金：

瑞士国家科学基金会;

关键词：

Contamination neighbourhood; Generalized linear model; Infinitesimal robustness; Lasso; Oracle estimator; Robust quasilikelihood; NONCONCAVE PENALIZED LIKELIHOOD; REGRESSION SHRINKAGE; CONFIDENCE-INTERVALS; ADAPTIVE LASSO; INFERENCE; ESTIMATORS; REGULARIZATION;

D O I：

10.1093/biomet/asx070

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Generalized linear models are popular for modelling a large variety of data. We consider variable selection through penalized methods by focusing on resistance issues in the presence of outlying data and other deviations from assumptions. We highlight the weaknesses of widely-used penalized M-estimators, propose a robust penalized quasilikelihood estimator, and show that it enjoys oracle properties in high dimensions and is stable in a neighbourhood of the model. We illustrate its finite-sample performance on simulated and real data.

引用

页码：31 / 44

页数：14

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