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).

引用

页码：409 / 420

页数：12

共 11 条

[1]

BIRGE L., 1997, FESTSCHRIFT L LECAM, P55

[2]

BOWMAN AW, 1984, BIOMETRIKA, V71, P353

[3] DISTRIBUTION-FREE LOWER BOUNDS IN DENSITY-ESTIMATION [J].