On marginal sliced inverse regression for ultrahigh dimensional model-free feature selection
type: Item
instance of: scholarly article
title: On marginal sliced inverse regression for ultrahigh dimensional model-free feature selection
zbMATH Open document ID: 1359.62218
DOI: 10.1214/15-AOS1424
author: Yuexiao Dong
author: Zhou Yu
author: Jun Shao
published in: The Annals of Statistics
publication date: 2017-02-13T00:00:00Z
review text: This paper aims to develop selection consistency for ultrahigh dimensional settings. An approach called marginal sliced inverse regression (SIR) is proposed for model-free feature screening and variable selection. Two distinct procedures, Dantzig selector and sparse precision matrix estimation, are incorporated to get two versions of sample level marginal SIR utilities. Both procedures lead to model-free variable selection consistency with predictor dimensionality \(p\) diverging at an exponential rate of the sample size \(n\). As a special case of marginal SIR, the correlation among the predictors is ignored and marginal independence SIR is proposed. Marginal independence SIR is closely related to many existing independence screening procedures in the literature, and achieves model-free screening consistency in the ultrahigh dimensional setting. The finite sample performances of the proposed procedures are studied through synthetic examples and an application to the small round blue cell tumour data is given.
reviewed by: Yuehua Wu
Mathematics Subject Classification ID: 62H20
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 62H99
Mathematics Subject Classification ID: 62J99
Mathematics Subject Classification ID: 62P10
zbMATH DE Number: 6684021
zbMATH Keywords: marginal coordinate test
zbMATH Keywords: sliced inverse regression
zbMATH Keywords: sufficient dimension reduction
zbMATH Keywords: sure independence screening
MaRDI profile type: Publication
full work available at URL: 15-aos1424
OpenAlex ID: W2551812373
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description: scientific article; zbMATH DE number 6684021