Robust estimation for survival partially linear single-index models

The partially linear single-index model is an interesting semiparametric model extended by the partially linear model and the single-index model, which supply a good balance between flexibility and parsimony. A robust estimation is proposed to fit the partially linear single-index model in case outliers may occur in the right censored response. This method provides a flexible way for modeling survival data. It is a profile M-estimation version and the estimation procedure involves transforming the censored data into synthetic data at first, then it results in fitting the common partially linear single-index models by a robust loss function. Asymptotic properties for the estimators of the linear and single-index coefficients and the optimal rate of convergence for the estimator of the nonparametric function are established. The finite sample performance of the proposed method is assessed by Monte Carlo simulation studies, and demonstrated by the analyses of PBC data and NCCTG lung cancer data.