Randomly censored partially linear single-index models

  • Authors:

  • Xuewen Lu;Tsung-Lin Cheng

  • Affiliations:

  • Department of Mathematics and Statistics, University of Calgary, Calgary, AB, Canada T2N 1N4;Department of Mathematics, National Changhua University of Education, Taiwan, ROC

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2007

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Abstract

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.