Multivariate Local Polynomial Fitting for A Probability Distribution Function and Its Partial Derivatives

Journal of Nonparametric Statistics

Volumn 13, Issue 1, 2000, Pages 77-94

  Abdous, B ^a   Bensaid, E ^b  

^a UNIVERSITÉ DU QUÉBEC À TROIS RIVIÈRES   (Canada)

^b UNIVERSITÉ LAVAL   (Canada)

Author keywords

Bandwidth smoothing matrix; Derivative estimation; Local polynomial fitting; Multivariate kernel estimators; Multivariate orthogonal polynomials

Indexed keywords

EID: 0347117735     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485250008832843     Document Type: Article

References (23)

1. Abdous, B., Berlinet, A. and Hengartner, N. (1999) A general theory for kernel estimation of smooth functionals of the distribution function and their derivatives. Technical report.
2. Berlinet, A. (1993) Hierarchies of higher order kernels. Probability Theory and Related Fields, 94, 489-504.
3. Delecroix, M., Simioni, S. and Thomas-Agnan, C. (1996) Functional estimation under shape restrictions. Journal of Nonparametric Statistics, 6, 69-89.
4. Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G. (1953) Higher Transcendental Functions. McGraw-Hill, New York.
5. Fan, J. and Gijbels, I. (1996) Local Polynomial Modelling and its Applications. Chapman and Hall, London.
6. Fernholz, L. T. (1983) Von Mises Calculus for statistical functionals. Lecture Notes in Statistics, 19, Springer Verlag, New York.
7. Fernholz, L. T. (1993) Smoothed versions of statistical functionals. In: New Directions in Statistical Data Analysis and Robustness, Morgenthaler, S. et al. Eds., pp. 61-72. Birkhauser Verlag.
8. Hill, P. D. (1985) Kernel estimation of a distribution function. Communications in Statistics, Theory and Methods, 14, 605-620.
9. Mammen, E. and Thomas-Agnan, C. (1999) Smoothing Splines and shape restrictions. Scandinavian Journal of Statistics, 26(2), 239-252.
10. Me Diarmid, C. (1989). On the method of bounded differences. In: Surveys in combinatorics. (Land. Math. Soc. Lect. Notes Ser., 141, 148-188) Cambridge University Press.
11. Lu, Z. (1996) Multivariate locally weighted polynomial fitting and partial derivative estimation. Journal of Multivariate Analysis, 59, 187-205.
12. Polansky, A. M. (1997) A smooth nonparametric approach to process capability. To appear in Quality and Reliability Engineering International.
13. Ruppert, D. and Wand, M. (1994) Multivariate locally weighted least squares regression. Annals of Statistics, 22(3), 1346-1370.
14. Scott, D. W. (1992) Multivariate Density Estimation: Theory, Practice, and Visualisation. New York: John Wiley.
15. Stein, E. M. (1971) Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, Princeton.
16. Wand, M. P. (1992) Error analysis for general multivariate kernel estimators. Journal of Nonparametric Statistics, 2, 1-15.
17. Wand, M. P. (1994) Fast computation of multivariate kernel estimators. Journal of Computational and Graphical Statistics, 3(4), 433-445.
18. Wand, M. P. and Jones, M. C. (1993) Comparison of smoothing parameterizations in bivariate kernel density estimation. Journal of the American Statistical Association, 88(422), 520-528.
19. Wand, M. P. and Jones, M. C. (1995) Kernel smoothing. Chapman and Hall, London.
20. Xu, Y. (1993) On multivariate orthogonal polynomials. SIAM Journal of Mathematical Analysis, 24(3), 783-794.
21. Xu, Y. (1997) On orthogonal polynomials in several variables. Fields Institute Communications, 14, 247-270.
22. d. Proceedings of the American Mathematical Society, 126(10), 3027-3036.
23. d. Transactions of the American Mathematical Society, 351(6), 2439-2458.