Linear hypothesis testing for high dimensional generalized linear models

Chengchun Shi, Rui Song, Zhao Chen and Runze Li

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: High dimensional testing; linear hypothesis; likelihood ratio statistics; score test; Wald test (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 33 pages
Date: 2019-10
New Economics Papers: this item is included in nep-ecm and nep-ore
References: Add references at CitEc
Citations: View citations in EconPapers (7)

Published in Annals of Statistics, October, 2019, 47(5), pp. 2671 - 2703. ISSN: 0090-5364

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:102108

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