An Asymptotically Optimal Window Selection Rule for Kernel Density Estimates
The Annals of Statistics · 1984 · Volume 12 · Issue 4
Abstract
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 Peter Hall.
Keywords
62G99, 62H99, asymptotic optimality, cross-validation, Kernel density estimate, poissonization, window selection rule
Enable JavaScript for citation tools and additional paper interactions.