Robust estimates in generalised varying-coefficient partially linear models

摘要

In this article, we introduce a family of robust estimates for the parametric and nonparametric components under a generalised semiparametric varying coefficient partially linear regression model, where the data are modelled by y_i｜(x_i,z_i, u_i) ～ F(.,μ_i,) with μ_i, = H(x_i~Tβ + z_i~Tα( u_i)), for some known distribution function F and link function H. A class of sieve robust estimation is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent; the convergence rate of the estimator for the unknown nonparametric component is obtained and the estimator for the unknown parameter is shown to be asymptotically normally distributed. Four simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real data set is used to illustrate our approach.