A Cross-Validation Bandwidth Choice for Kernel Density Estimates with Selection Biased Data
✍ Scribed by Colin O. Wu
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 376 KB
- Volume
- 61
- Category
- Article
- ISSN
- 0047-259X
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✦ Synopsis
This paper studies the risks and bandwidth choices of a kernel estimate of the underlying density when the data are obtained from s independent biased samples. The main results of this paper give the asymptotic representation of the integrated squared errors and the mean integrated squared errors of the estimate and establish a cross-validation criterion for bandwidth selection. This kernel density estimate is shown to be asymptotically superior to many other intuitive kernel density estimates. The data-driven cross-validation bandwidth is shown to be asymptotically optimal in the sense of Stone (1984, Ann. Statist. 12, 1285 1297). The finite sample properties of the cross-validation bandwidth are investigated through a Monte Carlo simulation.
1997 Academic Press
In the literature, distributions satisfying (1) are usually referred as the weighted distributions or the selection biased models. In this paper, we article no. MV971659 38 0047-259XÂ97 25.00