Linear hypothesis testing for high dimensional generalized linear models

Chengchun Shi, Rui Song, Zhao Chen, Runze Li

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)2671-2703
Number of pages33
JournalAnnals of Statistics
Volume47
Issue number5
DOIs
StatePublished - Jan 1 2019

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Linear Hypothesis
Generalized Linear Model
Hypothesis Testing
High-dimensional
Partial
Degree of freedom
Wald Test
Partial Likelihood
Local Alternatives
Penalized Likelihood
Testing Hypotheses
Concave function
Score Test
Hypothesis Test
Null Distribution
Empirical Analysis
Penalty Function
Regularization Method
Likelihood Ratio Test
Linear Constraints

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Shi, Chengchun ; Song, Rui ; Chen, Zhao ; Li, Runze. / Linear hypothesis testing for high dimensional generalized linear models. In: Annals of Statistics. 2019 ; Vol. 47, No. 5. pp. 2671-2703.
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Linear hypothesis testing for high dimensional generalized linear models. / Shi, Chengchun; Song, Rui; Chen, Zhao; Li, Runze.

In: Annals of Statistics, Vol. 47, No. 5, 01.01.2019, p. 2671-2703.

Research output: Contribution to journalArticle

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