Censored partial linear models and empirical likelihood

Consider the partial linear model Y-i = Y(i)(tau)beta + g(T-i) + epsilon (i ), i = 1,..., n, where beta is a p x 1 unknown parameter vector, g is an un known function, X-i's are p x 1 observable covariates, T-i's are other obse rvable covariates in [0, 1]. and Y-i's are the response variables. In this paper, we shall consider the problem of estimating beta and g and study the ir properties when the response variables Y-i are subject to random censori ng. First, the least square estimators for beta and kernel regression estim ator for g are proposed and their asymptotic properties are investigated. S econd. we shall apply the empirical likelihood method to the censored parti al 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 app roximate confidence region for beta. Some simulation studies are conducted to compare the empirical likelihood and normal approximation-based method. (C) 2001 Academic Press.