Two-stage local Walsh average estimation of generalized varying coefficient models

Abstract

In this paper we investigate the robust estimation of generalized varying coefficient models in which the unknown regression coefficients may change with different explanatory variables. Based on the B-spline series approximation and Walsh-average technique we develop an initial estimator for the unknown regression coefficient functions. By virtue of the initial estimator, the generalized varying coefficient model is reduced to a univariate nonparametric regression model. Then combining the local linear smooth and Walsh average technique we further propose a two-stage local linear Walsh-average estimator for the unknown regression coefficient functions. Under mild assumptions, we establish the large sample theory of the proposed estimators by utilizing the results of U-statistics and shows that the two-stage local linear Walsh-average estimator own an oracle property, namely the asymptotic normality of the two-stage local linear Walsh-average estimator of each coefficient function is not affected by other unknown coefficient functions. Extensive simulation studies are conducted to assess the finite sample performance, and a real example is analyzed to illustrate the proposed method.