论文信息 - Multivariate Local Fitting with General Basis Functions

Multivariate Local Fitting with General Basis Functions

SummaryIn this paper we combine the concepts of lcal smoothing and fitting with basis functions for multivariate predictor variables. We start with arbitrary basis functions and show that the asymptotic variance at interior points is independent of the choice of the basis. Moreover we calculate the asymptotic variance at boundary points. We are not able to compute the asymptotic bias since a Taylor theorem for arbitrary basis functions does not exist. For this reason we focus on basis functions without interactions and derive a Taylor theorem which covers this case. This theorem enables us to calculate the asymptotic bias for interior as well as for boundary points. We demonstrate how advantage can be taken of the idea of local fitting with general basis functions by means of a simulated data set, and also provide a data-driven tool to optimize the basis.

Jochen Einbeck | J. Einbeck

[1] M. Wand. Error analysis for general multtvariate kernel estimators , 1992 .

[2] M. C. Jones,et al. Comparison of Smoothing Parameterizations in Bivariate Kernel Density Estimation , 1993 .

[3] M. Wand,et al. Multivariate Locally Weighted Least Squares Regression , 1994 .

[4] L. Fahrmeir,et al. Multivariate statistische Verfahren , 1984 .

[5] W. Cleveland,et al. Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting , 1988 .

[6] Lijian Yang,et al. Multivariate bandwidth selection for local linear regression , 1999 .

[7] W. Cleveland. Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[8] E. Nadaraya. On Non-Parametric Estimates of Density Functions and Regression Curves , 1965 .

[9] G. S. Watson,et al. Smooth regression analysis , 1964 .

[10] B. Silverman,et al. Functional Data Analysis , 1997 .

[11] David R. Finston,et al. Kernel estimators for multivariate regression , 1993 .

[12] C. J. Stone,et al. Consistent Nonparametric Regression , 1977 .

[13] E. Nadaraya. On Estimating Regression , 1964 .

[14] Jianqing Fan. Design-adaptive Nonparametric Regression , 1992 .

[15] Jochen Einbeck. Local Fitting with General Basis Functions , 2001 .