Robust Estimation For Survival Partially Linear Single-index Models

The partially linear single-index model (PLSIM) 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 survival partially linear single-index model when outliers may occur in the right censored response. This method provides a flexible way for modeling the association between a response and a set of predic-tor variables when the response is right censored. 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 based on a robust objective function. We establish asymptotic properties for the resulting estimators of the linear and single-index coefficients, and the optimal rate of convergence for the nonparametric function estimator. The finite sample performance of the proposed method is assessed by Monte Carlo simulation studies, and demonstrated by the analyses of the PBC data, ACTG320data and NCCTG Lung Cancer Data.The contents of the paper is as follows. Section1is the introduction, will introduce some basis of the model and basic knowledge involved in this paper. Section2describes our robust estimation procedure. The asymptotic properties of these estimators are studied. Section3pro-vides a computation algorithm for solving the estimating functions and illustrates the estimation performance with Monte Carlo simulation results. Section4, we evaluate the proposed method by the PBC data, ACTG320data and NCCTG Lung Cancer data. All the conditions and tech-nical proofs of the main results are deferred to section5. Section6ends the paper with a brief discussion.