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Asymptotically optimal bandwidth selection rules for the kernel density estimator with dependent observations

โœ Scribed by Tae Yoon Kim

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
869 KB
Volume
59
Category
Article
ISSN
0378-3758

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โœฆ Synopsis

With mild restrictions placed on the kernel, kernel estimates of an unknown multivariatc density are investigated when the observed data are dependent. A modified cross validation rule, the simple 'leave-(2P + 1)-o&' version of simple cross validation, is considered for bandwidth selection. Under the mild assumption that the unknown density is bounded, this rule is shown to be asymptotically optimal under a geometric strong mixing condition. This strengthens recent results of Hart and Vieu (Ann. Stutist., 18 (1990)). The results are then extended to bandwidth selection problems associated to the Gibbs sampler.

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