VALID CONFIDENCE INTERVALS FOR POST-MODEL-SELECTION PREDICTORS

被引：24

作者：

Bachoc, Francois ^{[1
]}

Leeb, Hannes ^{[2
,3
]}

Potscher, Benedikt M. ^{[2
]}

机构：

[1] Univ Paul Sabatier, Dept Math, F-31062 Toulouse, France

[2] Univ Vienna, Dept Stat, A-1090 Vienna, Austria

[3] DataSci Univie, Vienna, Austria

来源：

ANNALS OF STATISTICS | 2019年 / 47卷 / 03期

基金：

奥地利科学基金会;

关键词：

Inference post-model-selection; confidence intervals; optimal post-model-selection predictors; nonstandard targets; linear regression; VARIABLE SELECTION; INFERENCE; ESTIMATORS; LIKELIHOOD;

D O I：

10.1214/18-AOS1721

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider inference post-model-selection in linear regression. In this setting, Berk et al. [Ann. Statist. 41 (2013a) 802-837] recently introduced a class of confidence sets, the so-called PoSI intervals, that cover a certain nonstandard quantity of interest with a user-specified minimal coverage probability, irrespective of the model selection procedure that is being used. In this paper, we generalize the PoSI intervals to confidence intervals for post-model-selection predictors.

引用

页码：1475 / 1504

页数：30

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