The Consistency of Automatic Kernel Density Estimates by Luc Devroye and Clark S . Penrod
نویسنده
چکیده
We consider the Parzen-Rosenblatt kernel density estimate on IP d with data-dependent smoothing factor. Sufficient conditions on the asymptotic behavior of the smoothing factor are given under which the estimate is pointwise consistent almost everywhere for all densities f to be estimated . When the smoothing factor is a function only of the sample size n, it is shown that these conditions are also necessary, a generalization of results by Deheuvels . The consistency of various automatic kernel density estimates is a simple consequence of these theorems.
منابع مشابه
A Note on the L1 Consistency of Variable Kernel Estimates
1 . Introduction . Most consistent nonparametric density estimates have a built-in smoothing parameter . Numerous schemes have been proposed (see, e.g ., references found in Rudemo, 1982 ; or Devroye and Penrod, 1984) for selecting the smoothing parameter as a function of the data only (a process called automatization), and for introducing locally adaptable smoothing parameters . In this note, ...
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