Local Linear Regression in Proportional Hazards Model with Censored Data

Abstract

In this article we study the method of nonparametric regression based on a transformation model, under which an unknown transformation of the survival time is nonlinearly, even more, nonparametrically, related to the covariates with various error distributions, which are parametrically specified with unknown parameters. Local linear approximations and locally weighted least squares are applied to obtain estimators for the effects of covariates with censored observations. We show that the estimators are consistent and asymptotically normal. This transformation model, coupled with local linear approximation techniques, provides many alternatives to the more general proportional hazards models with nonparametric covariates.

Keywords:

• Censored data
• Kernel estimator
• Local linear smoothing
• Nonparametric regression
• Transformation models

Mathematics Subject Classification:

• Primary 62J02
• Secondary 62N01