## The Annals of Statistics

### Local partial-likelihood estimation for lifetime data

#### Abstract

This paper considers a proportional hazards model, which allows one to examine the extent to which covariates interact nonlinearly with an exposure variable, for analysis of lifetime data. A local partial-likelihood technique is proposed to estimate nonlinear interactions. Asymptotic normality of the proposed estimator is established. The baseline hazard function, the bias and the variance of the local likelihood estimator are consistently estimated. In addition, a one-step local partial-likelihood estimator is presented to facilitate the computation of the proposed procedure and is demonstrated to be as efficient as the fully iterated local partial-likelihood estimator. Furthermore, a penalized local likelihood estimator is proposed to select important risk variables in the model. Numerical examples are used to illustrate the effectiveness of the proposed procedures.

#### Article information

Source
Ann. Statist., Volume 34, Number 1 (2006), 290-325.

Dates
First available in Project Euclid: 2 May 2006

https://projecteuclid.org/euclid.aos/1146576264

Digital Object Identifier
doi:10.1214/009053605000000796

Mathematical Reviews number (MathSciNet)
MR2275243

Zentralblatt MATH identifier
1091.62099

Subjects
Primary: 62G05: Estimation
Secondary: 62N01: Censored data models 62N02: Estimation

#### Citation

Fan, Jianqing; Lin, Huazhen; Zhou, Yong. Local partial-likelihood estimation for lifetime data. Ann. Statist. 34 (2006), no. 1, 290--325. doi:10.1214/009053605000000796. https://projecteuclid.org/euclid.aos/1146576264

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