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Linear hypothesis testing for high dimensional generalized linear models

Shi, Chengchun, Song, Rui, Chen, Zhao and Li, Runze (2019) Linear hypothesis testing for high dimensional generalized linear models. Annals of Statistics, 47 (5). 2671 - 2703. ISSN 0090-5364

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Identification Number: 10.1214/18-AOS1761

Abstract

This paper is concerned with testing linear hypotheses in high dimensional generalized linear models. To deal with linear hypotheses, we first propose the constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penalized Wald test. We show that the limiting null distributions of these three test statistics are χ2 distribution with the same degrees of freedom, and under local alternatives, they asymptotically follow noncentral χ2 distributions with the same degrees of freedom and noncentral parameter, provided the number of parameters involved in the test hypothesis grows to ∞ at a certain rate. Simulation studies are conducted to examine the finite sample performance of the proposed tests. Empirical analysis of a real data example is used to illustrate the proposed testing procedures.

Item Type: Article
Official URL: https://projecteuclid.org/all/euclid.aos
Additional Information: © 2019 Institute of Mathematical Statistics
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 15 Oct 2019 12:18
Last Modified: 25 Jan 2020 00:13
URI: http://eprints.lse.ac.uk/id/eprint/102108

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