Cross-Validation of Multivariate Densities
作者:
StephanR. Sain,
KeithA. Baggerly,
DavidW. Scott,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1994)
卷期:
Volume 89,
issue 427
页码: 807-817
ISSN:0162-1459
年代: 1994
DOI:10.1080/01621459.1994.10476814
出版商: Taylor & Francis Group
关键词: Biased and unbiased cross-validation;Bootstrap;Multivariate kernel density estimation
数据来源: Taylor
摘要:
In recent years, the focus of study in smoothing parameter selection for kernel density estimation has been on the univariate case, while multivariate kernel density estimation has been largely neglected. In part, this may be due to the perception that calibrating multivariate densities is substantially more difficult. In this article, we explicitly derive and compare multivariate versions of the bootstrap method of Taylor, the least-squares cross-validation method developed by Bowman and Rudemo, and a biased cross-validation method similar to that of Scott and Terrell for multivariate kernel estimation using the product kernel estimator. The theoretical behavior of these cross-validation algorithms is shown to improve (surprisingly) as the dimension increases, approaching the best rate ofO(n−1/2). Simulation studies suggest that the new biased cross-validation method performs quite well and with reasonable variability as compared to the other two methods. Bivariate examples with heart disease and ozone data are given to illustrate the behavior of these algorithms.
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