Quasi-universal bandwidth selection for kernel density estimators

被引：11
|
作者：
Wegkamp, MH [1 ]
机构：
[1] Yale Univ, Dept Stat, New Haven, CT 06520 USA
来源：
CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE | 1999年 / 27卷 / 02期
关键词：
asymptotic optimality; data splitting; empirical processes; kernel density estimators; projection estimators; universal bandwidth selection;
D O I：
10.2307/3315649
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Let (f) over cap(n), h denote the kernel density estimate based on a sample of size n drawn from an unknown density f. Using techniques from L-2 projection density estimators, the author shows how to construct a data-driven estimator (f) over cap(n), (H) which satisfies (sup)(bounded) lim sup(n --> infinity) integral E\(f) over cap(n),(H)(x) - f(x)\(2)dx/inf(h > 0)integral E\(f) over cap(n,h)(x)(\)(2)dx = 1. This paper is inspired by work of Stone (1984), Devroye and Lugosi (1996) and BirgC and Massart (1997).
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页码：409 / 420
页数：12
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