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Randomly censored partially linear single-index models. (English) Zbl 1139.62056

Summary: This paper proposes a method for estimation of a class of partially linear single-index models with randomly censored samples. The method provides a flexible way for modelling the association between a response and a set of predictor variables when the response variable is randomly censored. It presents a technique for “dimension reduction” in semiparametric censored regression models and generalizes the existing accelerated failure-time models for survival analysis.
The estimation procedure involves three stages: first, transform the censored data into synthetic data or pseudo-responses unbiasedly; second, obtain quasi-likelihood estimates of the regression coefficients in both linear and single-index components by an iteratively algorithm; finally, estimate the unknown nonparametric regression function using techniques for univariate censored nonparametric regression.
The estimators for the regression coefficients are shown to be jointly root-\(n\) consistent and asymptotically normal. In addition, the estimator for the unknown regression function is a local linear kernel regression estimator and can be estimated with the same efficiency as all the parameters are known. Monte Carlo simulations are conducted to illustrate the proposed methodology.

MSC:

62N02 Estimation in survival analysis and censored data
62N01 Censored data models
62G08 Nonparametric regression and quantile regression
62E20 Asymptotic distribution theory in statistics
65C05 Monte Carlo methods
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