Censored Quantile Regression For Partially Linear Varying Coefficient Models

Semiparametric models have good balance between parsimony and flexibility, thus they are often applied for survival data analyzing. In this paper, a class of partially linear quantile models which have varying coefficients are considered. We estimate the functional coefficients by spline function approximations. And a Kaplan-Meier estimator weighted censored quantile regression approach is proposed. The asymptotic properties of the proposed estimators are established. We use partially linear varying coefficient quantile regression models to analyze survival data. The survival time and the censoring variable need to be conditional independence given the covari-ates. In addition, our estimation procedure is easy to implement, it requires no specification of the error distributions. And our method can be achieved with R software in algorithm. The fi-nite sample performance of the proposed method is assessed by Monte Carlo simulation studies. And we show that the quantile regression model provides more comprehensive information than the other method by analyzing GBSG2 data set and prostate cancer dataset.The contents of the paper are as follows. In section 1, we introduce the development back-ground of our issue and provide the preliminary. In section 2, estimation and weighted methods are proposed, and asymptotic properties are established. In section 3, the finite sample per-formance of our method is investigated. In section 4, two real datasets are demonstrated by applying our approach. All the technical proofs of the main results are deferred to section 5. Section 6 ends the paper with a brief discussion.