Finite-sample variance of local polynomials: Analysis and solutions

Journal of the American Statistical Association

Volumn 91, Issue 433, 1996, Pages 267-275

  Seifert, Burkhardt ^a   Gasser, Theo ^a  

^a UNIVERSITY OF ZURICH   (Switzerland)

Author keywords

Nonparametric estimation; Nonparametric regression; Ridge regression; Smoothing; Weight function

Indexed keywords

EID: 0001652945     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1996.10476685     Document Type: Article

References (28)

1. Bhattacharya, P. K., and Müller, H.-G. (1993), “Asymptotics for Nonpara- metric Regression,” Sankhyä, Ser. A, 55, 420-441.
2. Bunke, H., and Bunke, O. (Eds.) (1986), Statistical Inference in Linear Models, Chichester, U.K.: John Wiley.
3. Chu, C. K., and Marron, J. S. (1991), “Choosing a Kernel Regression Estimator,” Statistical Science, 6, 404-433.
4. Cleveland, W. S. (1979), “Robust Locally Weighted Regression and Smoothing Scatterplots,” Journal of the American Statistical Association, 74, 829-836.
5. Dembo, A., and Karlin, S. (1992), “Poisson Approximations for r-Scan Processes,” Annals of Applied Probability, 2, 329-357.
6. Fan, J. (1993), “Local Linear Regression Smoothers and Their Minimax Efficiencies,” The Annals of Statistics, 21, 196-216.
7. Fan, J., Gasser, T., Gijbels, I., Brockmann, M., and Engel, J. (1993), “Local Polynomial Fitting: A Standard for Nonparametric Regression,” unpublished manuscript.
8. Fan, J., and Gijbels, I. (1992), “Variable Bandwidth and Local Linear Regression Smoothers,” The Annals of Statistics, 20, 2008-2036.
9. Fan, J., and Gijbels, I. (1994), “Adaptive Order Polynomial Fitting: Bandwidth Robustification and Bias Reduction,” unpublished manuscript.
10. Fan, J., and Marron, J. S. (1994), “Fast Implementations of Nonparametric Curve Estimators,” Journal of Computational and Graphical Statistics, 3, 35-56.
11. Friedman, J. H. (1984), “A Variable Span Smoother,” Technical Report 5, Stanford University, Dept, of Statistics.
12. Gasser, T., and Müller, H.-G. (1979), “Kernel Estimation of Regression Functions,” in Smoothing Techniques for Curve Estimation, Lecture Notes in Mathematics 757, New York: Springer, pp. 23-68.
13. Gasser, T., and Müller, H.-G. (1984), “Estimating Regression Functions and Their Derivatives by the Kernel Method,” Scandinavian Journal of Statistics, 11, 171-185.
14. Gasser, T., Müller, H.-G., and Mammitzsch, F. (1985), “Kernels for Nonparametric Curve Estimation,” Journal of the Royal Statistical Society, Ser. B, 47, 238-252.
15. Hall, P., and Marron, J. S. (1987), “On the Amount of Noise Inherent in Bandwidth Selection for a Kernel Density Estimator,” The Annals of Statistics, 15, 163-181.
16. Hastie, T., and Loader, C. (1993), “Local Regression: Automatic Kernel Carpentry,” Statistical Science, 8, 120-143.
17. Herrmann, E. (1995), “A Note on the Convolution-Type Kernel Regression Estimator,” unpublished manuscript.
18. Hotelling, H. (1961), “The Behavior of Some Standard Statistical Tests Under Nonstandard Conditions,” in Proceedings of the Forth Berkeley Symposium on Mathematical Statistics and Probability, 1, Berkeley, CA: University of California Press, pp. 319-359.
19. Lejeune, M. (1985), “Estimation Nonparamétrique par Noyaux: Régression Polynomiale Mobile,” Revue de Statistique Appliquée, 33, 43-68.
20. Müller, H.-G. (1988), Nonparametric Regression Analysis of Longitudinal Data, Lecture Notes in Statistics 46, Berlin: Springer.
21. Nadaraya, E. A. (1964), “On Estimating Regression,” Theory of Probability and Its Applications, 9, 141-142.
22. Reinsch, C. H. (1967), “Smoothing by Spline Functions,” Numerische Mathematik, 10, 177-183.
23. Ruppert, D., and Wand, M. P. (1994), “Multivariate Locally Weighted Least Squares Regression,” The Annals of Statistics, 22, 1346-1370.
24. Seifert, B., Brockmann, M., Engel, J., and Gasser, T. (1994), “Fast Algorithms for Nonparametric Curve Estimation,” Journal of Computational and Graphical Statistics, 3, 192-213.
25. Seifert, B., and Gasser, T. (1995), “Variance Properties of Local Polynomials and Ensuing Modifications,” Computational Statistics, to appear.
26. Stone, C. J. (1977), “Consistent Nonparametric Regression,” The Annals of Statistics, 5, 595-645.
27. Wahba, G. (1990), Spline Models for Observational Data, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 59, Philadelphia: Society for Industrial and Applied Mathematics.
28. Watson, G. S. (1964), “Smooth Regression Analysis,” Sankhyä, Ser. A, 26, 359-372.