Bias corrected bootstrap bandwidth selection. (English) Zbl 0889.62031
Summary: Current bandwidth selectors for kernel density estimation that are asymptotically optimal often prove less promising under more moderate sample sizes. The point of this paper is to derive a class of bandwidth selectors that attain optimal root-\(n\) convergence while still showing good results under small and moderate sample sizes. This is achieved by minimizing bias corrected smoothed bootstrap estimates of the mean integrated squared error. The degree of bias correction determines the rate of relative convergence of the resulting bandwidth. The bias correction targets finite sample bias rather than asymptotically leading terms, resulting in substantial improvements under smaller sample sizes.
In a simulation study, the new methods are compared to several of the currently most popular bandwidth selectors, including plug-in, cross-validation and other bootstrap rules. Practical implementation, and the choice of the oversmoothing bandwidth are discussed.
In a simulation study, the new methods are compared to several of the currently most popular bandwidth selectors, including plug-in, cross-validation and other bootstrap rules. Practical implementation, and the choice of the oversmoothing bandwidth are discussed.
MSC:
62G07 | Density estimation |
62G20 | Asymptotic properties of nonparametric inference |
62G09 | Nonparametric statistical resampling methods |
Keywords:
bandwidth selection; kernel density estimation; smoothed bootstrap estimates; bias correction; simulation studyReferences:
[1] | Billingsley P., Probability and Measure (1986) |
[2] | DOI: 10.1093/biomet/71.2.353 · doi:10.1093/biomet/71.2.353 |
[3] | DOI: 10.2307/2289609 · doi:10.2307/2289609 |
[4] | DOI: 10.1080/10485259408832605 · Zbl 1380.62148 · doi:10.1080/10485259408832605 |
[5] | Grund B. Polzehl J. Bias corrected bootstrap bandwidth selection Technical Report 611 School of Statistics, University of Minnesota 1996 |
[6] | DOI: 10.1016/0047-259X(90)90080-2 · Zbl 0722.62030 · doi:10.1016/0047-259X(90)90080-2 |
[7] | DOI: 10.1007/BF01192160 · Zbl 0742.62041 · doi:10.1007/BF01192160 |
[8] | DOI: 10.1007/BF01205233 · Zbl 0742.62042 · doi:10.1007/BF01205233 |
[9] | DOI: 10.1016/0167-7152(91)90163-L · doi:10.1016/0167-7152(91)90163-L |
[10] | DOI: 10.1214/aos/1176348378 · Zbl 0745.62033 · doi:10.1214/aos/1176348378 |
[11] | Jones M.C., Computational Statistics 11 pp 337– (1996) |
[12] | DOI: 10.1214/aos/1176348653 · Zbl 0746.62040 · doi:10.1214/aos/1176348653 |
[13] | DOI: 10.2307/2289526 · doi:10.2307/2289526 |
[14] | Rudemo M., Scandinavian Journal of Statistics 9 pp 65– (1982) · Zbl 0501.62028 |
[15] | Sheather S. J., J. R. Statist. Soc. B. 53 pp 683– (1991) |
[16] | Silverman B. W., Density Estimation (1986) · Zbl 0617.62042 · doi:10.1007/978-1-4899-3324-9 |
[17] | DOI: 10.1093/biomet/76.4.705 · Zbl 0678.62042 · doi:10.1093/biomet/76.4.705 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.