A general and fast convergent bandwidth selection method of kernel estimator

Journal of Nonparametric Statistics

Volumn 19, Issue 4-5, 2007, Pages 165-187

  Ahmad, Ibrahim A ^a   Amezziane, Mohamed ^b  

^a Assistant Professor in the University Libraries   (United States)

^b DEPAUL UNIVERSITY   (United States)

Author keywords

Bandwidth selection; M estimation; Nonparametric functional estimation; Rate of convergence; U statistics

Indexed keywords

EID: 37249011409     PISSN: 10485252     EISSN: 10290311     Source Type: Journal    
DOI: 10.1080/10485250701379848     Document Type: Article

References (38)

1. Rosenblatt, M., 1956, Remarks on some non-parametric estimates of a density function. Annals of Mathematical Statistics, 27, 642-669.
2. Devroye, L. and Györfi, L., 1985, Nonparametric Density Estimation: the LI View (New York: John Wiley & Sons).
3. Kanazawa, Y., 1993, Hellinger distance and Kullback-Leibler loss for the kernel density estimator. Statistics and Probability Letters, 18, 315-321.
4. Ahmad, I.A. and Mugdadi, A.R., 2006, A weighted Hellinger distance as an error criterion for bandwidth selection in kernel estimation. Journal of Nonparametric Statistics, 18, 215-226.
5. Wand, M.P. and Jones, M., 1995, Kernel Smoothing (London: Chapman and Hall).
6. Rudemo, M., 1982, Empirical choice of histograms and kernel density estimators. Scandinavian Journal of Statistics, 9, 65-78.
7. Bowman, A.W., 1984, An alternative method of cross-validation for the smoothing of density estimates. Biometrika, 71, 353-360.
8. Scott, D.W. and Terrell, G.R., 1987, Biased and unbiased cross-validation in density estimation. Journal of American Statistical Association, 82, 1131-1146.
9. Hall, P., 1983, Large sample optimality of least squares cross-validation in density estimation. The Annals of Statistics, 11, 1156-1174.
10. Stone, C.J., 1984, An asymptotically optimal window selection rule for kernel density estimates. Annals of Statistics, 12, 1285-1297.
11. Hall, P. and Marron, J.S., 1987, Extent to which least-squares cross-validation minimises integrated square error in nonparametric density estimation. Probability Theory and Related Fields, 74, 567-581.
12. Hall, P. and Marron, J.S., 1987, Estimation of integrated squared density derivatives. Statistics & Probability Letters, 6, 109-115.
13. Jones, M.C., Marron, J.S. and Sheather, S.J., 1996, A brief survey of bandwidth selection for density estimation. Journal of the American Statistical Association, 91, 401-407.
14. Ahmad, I.A. and Ran, I.R., 2004, Data based bandwidth selection in kernel density estimation with parametric start via kernel contrasts. Journal of Nonparametric. Statistics, 16, 841-877.
15. Woodroofe, M., 1970, On choosing a delta-sequence. Annals of Mathematical Statistics, 41, 1665-1671.
16. Ahmad, I.A., 1976, On asymptotic properties of an estimate of a functional of a probability density. Scandinavian Actuarial Journal, 3, 176-182.
17. Sheather, S. and Jones, M., 1991, A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society, Series B (Methodological), 55, 683-690.
18. Chiu, S., 1992, An automatic bandwidth selector for kernel density estimation. Biometrika, 79, 771-782.
19. Engel, J., Herrmann, E. and Gasser, T., 1994, An iterative bandwidth selector for kernel estimation of densities and their derivatives. Journal of Nonparametric Statistics, 4, 21-34.
20. Park, B.U. and Marron, J.S., 1992, On the use of pilot estimators in bandwidth selection. Journal of Nonparametric Statistics, 1, 231-240.
21. Loader, C.R., 1999, Bandwidth selection: classical or plug-in? The Annals of Statistics, 27, 415-438.
22. Hardle, W., Müller, M., Sperlich, S. and Werwatz, A., 2004, Nonparametric and Semiparametric. Models (New York: Springer-Verlag).
23. Wasserman, L., 2004, All of Statistics (New York: Springer-Verlag).
24. Nadaraya, È.A., 1964, Some new estimates for distribution functions. Theory of Probability and its Applications, 9, 497-500.
25. Bowman, A.W., Hall, P. and Prvan, T., 1998, Bandwidth selection for the smoothing of distribution functions. Biometrika, 85, 799-808.
26. Sarda, P., 1993, Smoothing parameter selection for smooth distribution functions. Journal of Statistical Planning and Inference, 35, 65-75.
27. Altman, N. and Léger, C., 1995, Bandwidth selection for kernel distribution function estimation. Journal of Statistical Planning and Inference, 46, 195-214.
28. Bickel and Ritov (1988).
29. Jones, M.C. and Sheather, S.J., 1991, Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives. Statistics & Probability Letters, 11, 511-514.
30. Chiu, S., 1991, Bandwidth selection for kernel density estimation. Annals of Statistics, 19, 1883-1905.
31. Wu, T., 1995, Adaptive root n estimates of integrated squared density derivatives. Annals of Statistics, 23, 1474-1495.
32. Hall, P. and Marron, J.S., 1991, Local minima in cross-validation functions. Journal of the Royal Statistical Society, Series B (Methodological), 53, 245-252.
33. Hall, P., 1984, Central limit theorem for integrated square error of multivariate nonparametric density estimators. Journal of Multivariate Analysis, 14, 1-16.
34. Silverman, B.W., 1986, Density Estimation for Statistics and Data Analysis (London: Chapman and Hall).
35. Park, B. and Marron, J.S., 1990, Comparison of data-driven bandwidth selectors. Journal of the American Statistical Association, 85, 66-72.
36. Polansky, A.M. and Baker, E.R., 2000, Multistage plug-in bandwidth selection for kernel distribution function estimates. Journal of Statistical Computation and Simulation, 65, 63-80.
37. Tenreiro, C., 2003, On the asymptotic normality of multistage integrated density derivatives kernel estimators. Statistics and Probability Letters, 53, 283-292.
38. Van der Vaart, A.W., 1998, Asymptotic Statistics (Cambridge: Cambridge University Press).