Local asymptotic inference for nonparametric regression with censored survival data

Yanyan Liu, Guangcai Mao, Xingqiu Zhao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

We consider a penalised nonparametric estimation of the relative risk function in the Cox proportional hazards model for survival data with right censoring. We derive the convergence rate, functional Bahadur representation (FBR) and local asymptotic normality of the nonparametric estimator by using reproducing kernel Hilbert space, counting process and empirical process theory. The new theoretical results fill the gap in the smoothing splines literature for nonparametric estimation in survival models. Furthermore, we construct the corresponding local confidence intervals by the bootstrap method. Extensive simulation studies are conducted to validate the proposed method and compare with the Bayesian confidence intervals, and a data example from the Stanford heart transplant study is provided for illustration.

Original languageEnglish
Pages (from-to)1015-1028
Number of pages14
JournalJournal of Nonparametric Statistics
Volume32
Issue number4
DOIs
Publication statusE-pub ahead of print - 30 Oct 2020

Keywords

  • Censored survival data
  • Cox proportional hazards model
  • functional Bahadur representation
  • nonparametric statistical inference
  • reproducing kernel Hilbert space

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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