Multivariate locally weighted polynomial fitting and partial derivative estimation

Journal of Multivariate Analysis

Volumn 59, Issue 2, 1996, Pages 187-205

  Lu, Zhan Qian ^a  

^a NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

Asymptotic bias; Asymptotic variance; Joint asymptotic normality; Kernel estimator; Locally weighted regression; Nonparametric regression

Indexed keywords

EID: 0030295954     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1996.0060     Document Type: Article

References (20)

1. [1] Chu, C. K., and Marron, J. S. (1991). Choosing a kernel estimator (with discussions). Statist. Sci. 6, No. 4 404-436.
2. [2] Cleveland, W. (1979). Robust locally weighted regression and smoothing scatterplots. J. Amer. Statist. Assoc. 74, No. 368 829-836.
3. [3] Cleveland, W., and Devlin, S. (1988). Locally weighted regression: An approach to regression analysis by local fitting. J. Amer. Statist. Assoc. 83, No. 403 596-610.
4. [4] Fan, J. (1993). Local linear regression smoothers and their minimax efficiencies. Ann of Statist. 21, No. 1 196-216.
5. [5] Fan, J., and Gijbels, I. (1992). Variable bandwith and local linear regression smoothers. Ann. of Statist. 20, No. 4 2008-2036.
6. [6] Gasser, T., and Müller, H. G. (1979). Kernel estimation of regression functions. Smoothing Techniques for Curve Estimation. Lecture Notes in Math., Vol. 757, pp. 23-68. Springer-Verlag New York.
7. [7] Härdle, W. (1990). Applied Nonparametric Regression. Cambridge Univ. Press, Boston.
8. [8] Magnus, J. R., and Neudecker, H. (1980). The elimination matrix: Some lemmas and applications. SIAM J. Alg. Disc. Methods 1, No. 4 422-449.
9. [9] Lu, Z. Q. (1994). Estimating Lyapunov Exponents in Chaotic Time Series with Locally Weighted Regression. Ph.D. dissertation. University of North Carolina, Chapel Hill.
10. [10] Lu, Z. (1995a). Multivariate locally weighted polynomial fit and partial derivative estimation. Unpublished.
11. [11] Lu, Z. Q. (1995b). Statistical estimation of local Lyapunov exponents: Toward characterizing predictability in nonlinear systems. Submitted.
12. [12] McCaffrey, D., Nychka, D., Ellner, S., and Gallant, A. R. (1992). Estimating Lyapunov exponents with nonparametric regression. J. Amer. Statist. Soc. 87, No. 419 682-695.
13. [13] Müller, H.-G. (1988). Nonparametric Regression Analysis of Longitudinal Data. Springer-Verlag, Berlin.
14. [14] Nadaraya, E. A. (1964). On estimating regression. Theory Probab. Appl. 9 141-142.
15. [15] Rao, C. R. (1973). Linear Statistical Inference and Its Applications, 2nd ed. Wiley, New York.
16. [16] Ruppert, D., and Wand, M. P. (1994). Multivariate locally weighted least squares regression. Ann. Statist. 22, No. 3 1346-1370.
17. [17] Serfling, R. J. (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York.
18. [18] Stone, C. J. (1977). Consistent nonparametric regression (with discussions). Ann. of Statist. 5, No. 4 595-645.
19. [19] Stone, C. J. (1980). Optimal rate of convergence for nonparametric estimators. Ann. of Statist. 8, No. 6 1348-1360.
20. [20] Watson, G. S. (1964). Smooth regression analysis. Sankhyā Ser.A 26 359-372.