Selective inference with a randomized response
type: Item
instance of: scholarly article
title: Selective inference with a randomized response
zbMATH Open document ID: 1392.62144
DOI: 10.1214/17-AOS1564
author: Xiaoying Tian
author: Jonathan Taylor
published in: The Annals of Statistics
publication date: 2018-05-18T00:00:00Z
full work available at URL: https://arxiv.org/abs/1507.06739
review text: The authors investigate general selective inference with randomized response in model selection. They introduce the selective likelihood ratio and a framework of asymptotic analysis for selective models. The problems of consistent estimation and week convergence are studied. It is shown that randomization selection schemes lead to an increase in test powers. Linear regression models are used as examples. It is shown that the central limit theorem holds true under mild conditions on the selective distributions. This makes it possible to develop asymptotic selective inference in nonparametric settings. Finally, the paper discusses two extensions to multiple randomized selections: selective inference after cross-validation for LASSO and collaborative selective inference. Some additional sampling schemes and all proofs are given in the supplementary materials.
Mathematics Subject Classification ID: 62G99
Mathematics Subject Classification ID: 62J07
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 6870276
zbMATH Keywords: selective inference
zbMATH Keywords: nonparametric
zbMATH Keywords: differential privacy
zbMATH Keywords: central limit theorem
reviewed by: Andriy Olenko
describes a project that uses: covTest
describes a project that uses: tmg
MaRDI profile type: Publication
arXiv ID: 1507.06739
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description: scientific article