Efficient estimation of the partly linear additive Cox model

Jian Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

97 Citations (Scopus)

Abstract

The partly linear additive Cox model is an extension of the (linear) Cox model and allows flexible modeling of covariate effects semiparametrically. We study asymptotic properties of the maximum partial likelihood estimator of this model with right-censored data using polynomial splines. We show that, with a range of choices of the smoothing parameter (the number of spline basis functions) required for estimation of the nonparametric components, the estimator of the finite-dimensional regression parameter is root-n consistent, asymptotically normal and achieves the semiparametric information bound. Rates of convergence for the estimators of the nonparametric components are obtained. They are comparable to the rates in nonparametric regression. Implementation of the estimation approach can be done easily and is illustrated by using a simulated example.
Original languageEnglish
Pages (from-to)1536-1563
Number of pages28
JournalAnnals of Statistics
Volume27
Issue number5
Publication statusPublished - 1 Oct 1999
Externally publishedYes

Keywords

  • Additive regression
  • Asymptotic normality
  • Partial likelihood
  • Polynomial splines
  • Projection
  • Rate of convergence
  • Right-censored date
  • Semiparametric information bound

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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