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Testing and confidence intervals for high dimensional proportional hazards models
Author(s) -
Fang Ethan X.,
Ning Yang,
Liu Han
Publication year - 2017
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12224
Subject(s) - pointwise , confidence interval , mathematics , statistics , consistency (knowledge bases) , robust confidence intervals , confidence region , confidence distribution , wald test , proportional hazards model , asymptotic distribution , score , hazard ratio , hazard , statistical hypothesis testing , estimator , mathematical analysis , geometry , chemistry , organic chemistry
Summary The paper considers the problem of hypothesis testing and confidence intervals in high dimensional proportional hazards models. Motivated by a geometric projection principle, we propose a unified likelihood ratio inferential framework, including score, Wald and partial likelihood ratio statistics for hypothesis testing. Without assuming model selection consistency, we derive the asymptotic distributions of these test statistics, establish their semiparametric optimality and conduct power analysis under Pitman alternatives. We also develop new procedures to construct pointwise confidence intervals for the baseline hazard function and conditional hazard function. Simulation studies show that all tests proposed perform well in controlling type I errors. Moreover, the partial likelihood ratio test is empirically more powerful than the other tests. The methods proposed are illustrated by an example of a gene expression data set.