Varying coefficient models having different smoothing variables with randomly censored data

The varying coefficient model is a useful alternative to the classical linear model, since the former model is much richer and more flexible than the latter. We propose estimators of the coefficient functions for the varying coefficient model in the case where different coefficient functions depend on different covariates and the response is subject to random right censoring. Since our model has an additive structure and requires multivariate smoothing we employ a smooth backfitting technique, that is known to be an effective way to avoid "the curse of dimensionality" in structured nonparametric models. The estimators are based on synthetic data obtained by an unbiased transformation. The asymptotic normality of the estimators is established, a simulation study illustrates the reliability of our estimators, and the estimation procedure is applied to data on drug abuse.