Under the condition that the total distribution function is continuous and bounded on （ -∞,∞ ）, we constructed estimations for distribution and hazard functions with local polynomial method, and obtained the rate ...Under the condition that the total distribution function is continuous and bounded on （ -∞,∞ ）, we constructed estimations for distribution and hazard functions with local polynomial method, and obtained the rate of strong convergence of the estimations.展开更多
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
文摘Under the condition that the total distribution function is continuous and bounded on （ -∞,∞ ）, we constructed estimations for distribution and hazard functions with local polynomial method, and obtained the rate of strong convergence of the estimations.
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.
