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Local partial-likelihood estimation for lifetime data. (English) Zbl 1091.62099
Summary: 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.

62N02 Estimation in survival analysis and censored data
62G20 Asymptotic properties of nonparametric inference
62G05 Nonparametric estimation
62N01 Censored data models
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