Penalized generalized empirical likelihood with a diverging number of general estimating equations for censored data

Niansheng Tang, Xiaodong Yan, Xingqiu Zhao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

Abstract

This article considers simultaneous variable selection and parameter estimation as well as hypothesis testing in censored survival models where a parametric likelihood is not available. For the problem, we utilize certain growing dimensional general estimating equations and propose a penalized generalized empirical likelihood, where the general estimating equations are constructed based on the semiparametric efficiency bound of estimation with given moment conditions. The proposed penalized generalized empirical likelihood estimators enjoy the oracle properties, and the estimator of any fixed dimensional vector of nonzero parameters achieves the semiparametric efficiency bound asymptotically. Furthermore, we show that the penalized generalized empirical likelihood ratio test statistic has an asymptotic central chi-square distribution. The conditions of local and restricted global optimality of weighted penalized generalized empirical likelihood estimators are also discussed. We present a two-layer iterative algorithm for efficient implementation, and investigate its convergence property. The performance of the proposed methods is demonstrated by extensive simulation studies, and a real data example is provided for illustration.

Original languageEnglish
Pages (from-to)607-627
Number of pages21
JournalAnnals of Statistics
Volume48
Issue number1
DOIs
Publication statusPublished - Feb 2020

Keywords

  • Censored survival data
  • Oracle property
  • Penalized generalized empirical likelihood
  • Penalized generalized empirical likelihood ratio test
  • Semiparametric efficiency

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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