Varying coefficients partially linear models with randomly censored data (Preliminary and incomplete)

This paper considers the problem of estimation and inference in semiparametric varying coefficients models when the response variable is subject to random censoring. The paper proposes an estimator based on combining inverse probability censoring weighting and profile least squares estimation. The resulting estimator is shown to be asymptotically normal. The paper proposes three test statistics with an asymptotic chi-squared calibration that can be used to test linear restrictions on the parametric components.The paper also considers the important issue of correct specification of the model and proposes a nonsmoothing test based on a Cramer-von Mises type of statistic. Monte Carlo simulations illustrate the finite sample properties of the estimators and test statistics.