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An asymptotically optimal window selection rule for kernel density estimates. (English) Zbl 0599.62052
Kernel estimates of an unknown multivariate density are investigated, with mild restrictions being placed on the kernel. A window selection rule is considered, which can be interpreted in terms of cross- validation. Under the mild assumption that the unknown density and its one-dimensional marginals are bounded, the rule is shown to be asymptotically optimal. This strengthens recent results of P. Hall [Multivariate analysis, Proc. 6th Int. Symp., Pittsburgh/Pa. 1983, Multivariate Anal. 6, 289-309 (1985; Zbl 0592.62042); Ann. Stat. 11, 1156-1174 (1983; see the preceding review, Zbl 0599.62051)].

MSC:
62G05Nonparametric estimation
62G99Nonparametric inference
62H99Multivariate analysis
62H12Multivariate estimation