This paper considers a nonparametric varying coefficient regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the coefficient functions. Unde...This paper considers a nonparametric varying coefficient regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the coefficient functions. Under mild regularity assumptions,the global convergence rates of the B-spline estimators of the unknown coefficient functions are established. Asymptotic results show that our B-spline estimators achieve the optimal convergence rate. The asymptotic distributions of the B-spline estimators of the unknown coefficient functions are also derived. A procedure for selecting smoothing parameters is given. Finite sample properties of our procedures are studied through Monte Carlo simulations. Application of the proposed method is demonstrated by examining voting behaviors across US counties in the 1980 presidential election.展开更多
High-order dispersion coefficients C9, C11, C12, and C13 for the ground-state alkali-metals were calculated by combining the 1-dependent model potential of alkali-metal atoms and linear variation method based on B-spl...High-order dispersion coefficients C9, C11, C12, and C13 for the ground-state alkali-metals were calculated by combining the 1-dependent model potential of alkali-metal atoms and linear variation method based on B-spline basis functions. The results were compared.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
基金supported by National Natural Science Foundation of China (Grant No. 10671089)China Postdoctoral Science Foundation and Jiangsu Planned Projects for Postdoctoral Research Funds
文摘This paper considers a nonparametric varying coefficient regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the coefficient functions. Under mild regularity assumptions,the global convergence rates of the B-spline estimators of the unknown coefficient functions are established. Asymptotic results show that our B-spline estimators achieve the optimal convergence rate. The asymptotic distributions of the B-spline estimators of the unknown coefficient functions are also derived. A procedure for selecting smoothing parameters is given. Finite sample properties of our procedures are studied through Monte Carlo simulations. Application of the proposed method is demonstrated by examining voting behaviors across US counties in the 1980 presidential election.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10947101 and 11074070, the Science and Technology Foundation of Guizhou Province under Grant Nos. J[201212345 and LKZS[2012]02, the Hunan Provincial Natural Science Foundation under Grant No. 10J J4001, the Special Foundation of Governor of Guizhou Province for Science and Technology and Education Talents under Grant No. [2012]87, the Doctor Foundation of Zunyi Normal College under Grant Nos. 2012BSJJ17 and the Key Support Discipline of Guizhou province under Grant No. [20111275. Ding＇s work is supported by Hunan Provincial Natural Science Foundation under Grant No. 11JJ3014 and the Scientific Research Fund of Hunan Provincial Education Department under Grant No. 11B067
文摘High-order dispersion coefficients C9, C11, C12, and C13 for the ground-state alkali-metals were calculated by combining the 1-dependent model potential of alkali-metal atoms and linear variation method based on B-spline basis functions. The results were compared.
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.
