L2 version of the double kernel method

被引：4

作者：

Abdous, B ^{[1
]}

机构：

[1] Univ Quebec Trois Rivieres, Dept Math & Informat, Trois Rivieres, PQ G9A 5H7, Canada

来源：

STATISTICS | 1999年 / 32卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

kernel density estimate; double kernel method; bandwidth; higher order kernels; rate of convergence;

D O I：

10.1080/02331889908802666

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：

Consider two kernel density estimates having the same bandwidth but two different kernels. The criterion which minimizes the LI distance between these two estimates is known as the double kernel method. In this work, instead of the LI distance, we use the L-2 one. Asymptotic behavior of this criterion and the corresponding bandwidth are investigated. It is shown that the L-2 double kernel method and the least-squares cross-validation technique have almost the same properties. An implementation of the method is also proposed.

引用

页码：249 / 266

页数：18

共 22 条

[1] COMPUTATIONALLY EFFICIENT CLASSES OF HIGHER-ORDER KERNEL FUNCTIONS [J].

ABDOUS, B .

CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE, 1995, 23 (01) :21-27

[2] HIERARCHIES OF HIGHER-ORDER KERNELS [J].

BERLINET, A .

PROBABILITY THEORY AND RELATED FIELDS, 1993, 94 (04) :489-504

[3]

Berlinet A., 1994, Publ. Inst. Statist. Univ. Paris, V38, P3

[4] A COMPARATIVE-STUDY OF SEVERAL SMOOTHING METHODS IN DENSITY-ESTIMATION [J].

CAO, R ;

CUEVAS, A ;

MANTEIGA, WG .

COMPUTATIONAL STATISTICS & DATA ANALYSIS, 1994, 17 (02) :153-176

[5]

DEVROYE L, 1989, ANN I H POINCARE-PR, V25, P533

[6] A COMPARATIVE-STUDY OF SOME BIAS CORRECTION TECHNIQUES FOR KERNEL-BASED DENSITY ESTIMATORS [J].

FOSTER, P .

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 1995, 51 (2-4) :137-152

[7]

HALL P, 1992, J ROY STAT SOC B MET, V54, P475

[8] LARGE SAMPLE OPTIMALITY OF LEAST-SQUARES CROSS-VALIDATION IN DENSITY-ESTIMATION [J].

HALL, P .

ANNALS OF STATISTICS, 1983, 11 (04) :1156-1174

[9] SMOOTHED CROSS-VALIDATION [J].

HALL, P ;

MARRON, JS ;

PARK, BU .

PROBABILITY THEORY AND RELATED FIELDS, 1992, 92 (01) :1-20

[10] CENTRAL LIMIT-THEOREM FOR INTEGRATED SQUARE ERROR OF MULTIVARIATE NONPARAMETRIC DENSITY ESTIMATORS [J].

HALL, P .

JOURNAL OF MULTIVARIATE ANALYSIS, 1984, 14 (01) :1-16

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