Censored Partial Linear Models and Empirical Likelihood

Consider the partial linear model Yi=X[tau]i[beta]+g(Ti)+[var epsilon]i, i=1, ..., n, where [beta] is a p-1 unknown parameter vector, g is an unknown function, Xi's are p-1 observable covariates, Ti's are other observable covariates in [0, 1], and Yi's are the response variables. In this paper, we shall consider the problem of estimating [beta] and g and study their properties when the response variables Yi are subject to random censoring. First, the least square estimators for [beta] and kernel regression estimator for g are proposed and their asymptotic properties are investigated. Second, we shall apply the empirical likelihood method to the censored partial linear model. In particular, an empirical log-likelihood ratio for [beta] is proposed and shown to have a limiting distribution of a weighted sum of independent chi-square distributions, which can be used to construct an approximate confidence region for [beta]. Some simulation studies are conducted to compare the empirical likelihood and normal approximation-based method.