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

共 36 条

[1] Hybrid and Size-Corrected Subsampling Methods
Andrews, Donald W. K.
Guggenberger, Patrik
[J]. ECONOMETRICA, 2009, 77 (03) : 721 - 762
[2] [Anonymous], 2015, J HEPATOL, V63, P237, DOI 10.1016/j.jhep.2015.04.006
[3] BACHOC F., 2019, VALID CONFIDENCE I S, DOI [10.1214/18-AOS1721SUPP, DOI 10.1214/18-AOS1721SUPP]
[4] Belloni A., 2011, ADV EC ECONOMETRICS, VIII, P245
[5] Inference on Treatment Effects after Selection among High-Dimensional ControlsaEuro
Belloni, Alexandre
Chernozhukov, Victor
Hansen, Christian
[J]. REVIEW OF ECONOMIC STUDIES, 2014, 81 (02) : 608 - 650
[6] BERK R., 2013, VALID POSTSELE UNPUB
[7] VALID POST-SELECTION INFERENCE
Berk, Richard
Brown, Lawrence
Buja, Andreas
Zhang, Kai
Zhao, Linda
[J]. ANNALS OF STATISTICS, 2013, 41 (02) : 802 - 837
[8] Variable selection via nonconcave penalized likelihood and its oracle properties
Fan, JQ
Li, RZ
[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2001, 96 (456) : 1348 - 1360
[9] Fithian William., 2015, OPTIMAL INFERENCE MO
[10] Persistence in high-dimensional linear predictor selection and the virtue of overparametrization
Greenshtein, E
Ritov, Y
[J]. BERNOULLI, 2004, 10 (06) : 971 - 988

← 1 2 3 4 →