Multistage plug-in bandwidth selection for kernel distribution function estimates

Journal of Statistical Computation and Simulation

Volumn 65, Issue 1, 2000, Pages 63-80

  Polansky, Alan M ^a   Baker, Edsel R ^b  

^a NORTHERN ILLINOIS UNIVERSITY   (United States)

^b University of Florida ^*  (United States)

Author keywords

Normal reference rule; Oversmoothing bandwidth; Plug in rule; Smoothing; Squared error loss; Survival function

Indexed keywords

EID: 0034348941     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949650008811990     Document Type: Article

References (30)

1. Abdous, B. (1993) Note on the minimum mean integrated squared error of kernel estimates of a distribution function and its derivatives, Communications in Statistics, Theory and Methods, 22, 603-609.
2. Altman, N. and Leger, C. (1995) Bandwidth selection for kernel distribution function estimation, Journal of Statistical Planning and Inference, 46, 195-214.
3. Azzalini, A. (1981) A note on the estimation of a distribution function and quantiles by a kernel method, Biometrika, 68, 326-328.
4. Bowman, A., Hall, P. and Prvan, T. (1998) Bandwidth selection for the smoothing of distribution functions, Biometrika, 85, 799-808.
5. Chiu, S.-T. (1991) Bandwidth selection for kernel density estimation, Annals of Statistics, 19, 1883-1905.
6. Engel, J., Herrmann, E. and Gasser, T. (1995) An iterative bandwidth selector for kernel estimation of densities and their derivatives, Journal of Nonparametric Statistics, 4, 21-34.
7. Hall, P. and Marron, J. S. (1987) Estimation of integrated squared density derivatives, Statistics and Probability Letters, 6, 109-115.
8. Hill, P. D. (1985) Kernel estimation of a distribution function, Communications in Statistics, Theory and Methods, 14, 605-620.
9. Hoel, D. G. (1972) A representation of mortality data by competing risks, Biometrics, 28, 475-488.
10. Jones, M. C. (1990) The performance of kernel density functions in kernel distribution function estimation, Statistics and Probability Letters, 9, 129-132.
11. Jones, M. C. and Sheather, S. J. (1991) Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives, Statistics and Probability Letters, 11, 511-514.
12. Marron, J. S. and Wand, M. P. (1992) Exact mean integrated squared error, The Annals of Statistics, 20, 712-736.
13. Nadaraya, E. A. (1964) Some new estimates for distribution functions, Theory of Probability and its Applications, 9, 497-500.
14. Nadaraya, E. A. (1974) On the integral mean square error of some nonparametric estimates for the density function, Theory of Probability and its Applications, 19, 133-141.
15. Park, B. U. and Marron, J. S. (1990) Comparison of data-driven bandwidth selectors, Journal of the American Statistical Association, 85, 66-72.
16. Polansky, A. M. (1998) A smooth nonparametric approach to process capability, Quality and Reliability Engineering International, 14, 43-48.
17. Polansky, A. M. (1999) An algorithm for computing a smooth nonparametric process capability estimate, Journal of Quality Technology, to appear.
18. Sarda, P. (1993) Smoothing parameter selection for smooth distribution functions, Journal of Statistical Planning and Inference, 35, 65-75.
19. Serfling, R. J. (1980) Approximation Theorems of Mathematical Statistics, John Wiley and Sons, New York.
20. Sheather, S. J. and Jones, M. C. (1991) A reliable data-based bandwidth selection method for kernel density estimation, Journal of the Royal Statistical Society, Series B, 53, 683-690.
21. Shirahata, S. and Chu, I.-S. (1992) Integrated squared error of kernel-type estimator of distribution function, Annals of the Institute of Statistical Mathematics, 44, 579-591.
22. Silverman, B. W. (1986) Density Estimation for Statistics and Data Analysis, Chapman and Hall, London.
23. Singh, R. S., Gasser, T. and Prasad, B. (1983) Nonparametric estimates of distribution functions, Communications in Statistics, Theory and Methods, 12, 2095-2108.
24. Swanepoel, J. W. H. (1988) Mean integrated squared error properties and optimal kernels when estimating a distribution function, Communications in Statistics, Theory and Methods, 17, 3785-3799.
25. Terrell, G. R. (1990) The maximal smoothing principle in density estimation, Journal of the American Statistical Association, 85, 470-477.
26. Terrell, G. R. and Scott, D. W. (1985) Oversmoothed nonparametric density estimates, Journal of the American Statistical Association, 80, 209-214.
27. Wand, M. P. (1997) Data-based choice of histogram bin width, The American Statistician, 51, 59-64.
28. Wand, M. P. and Jones, M. C. (1995) Kernel Smoothing, Chapman and Hall, London.
29. White, J., Riethof, M. and Kushnir, I. (1960) Estimation of microcrystalline wax in beeswax, Journal of the Association of Official Analytical Chemists, 43, 781-790.
30. Woodroofe, M. (1970) On choosing a delta-sequence, Annals of Mathematical Statistics, 41, 1665-1671.