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 a...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.展开更多
基金Supported by the National Natural Science Foundation of China(NSFC)(No.11471203)the Graduate Innovation Fund of Shanghai University of Finance and Economics(CXJJ-2013-459)
文摘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.
