On choosing a non-integer resolution level when using wavelet methods

被引：19

作者：

Hall, P

Nason, GP

机构：

[1] AUSTRALIAN NATL UNIV,CTR MATH & APPLICAT,CANBERRA,ACT 0200,AUSTRALIA

[2] UNIV BRISTOL,DEPT MATH,BRISTOL BS8 1TW,AVON,ENGLAND

来源：

STATISTICS & PROBABILITY LETTERS | 1997年 / 34卷 / 01期

关键词：

bandwidth; curve estimation; density estimation; dyadic expansion; mean squared error; Kernel estimator; nonparametric regression;

D O I：

10.1016/S0167-7152(96)00159-9

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：

In curve estimation using wavelet methods it is common to select the resolution level to be an integer, so as to exploit the computational advantages of the pyramid or cascade algorithm. This choice, however, can produce a noticeable amount of either oversmoothing or undersmoothing. Its analogue for estimation by kernel methods is to restrict the bandwidth to be an integer power of 1/2, which would seldom be acceptable. In this note we quantify the advantages of non-integer resolution levels.

引用

页码：5 / 11

页数：7

共 10 条

[1]

AUSCHER P, 1992, WAVELETS THEIR APPL, P439

[2]

AUSCHER P, 1989, THESIS U PARIS DAUPH

[3]

Brent R. P., 2002, Algorithms for Minimization without Derivatives

[4]

DONOHO DL, 1995, J ROY STAT SOC B MET, V57, P301

[5] BOOTSTRAP CHOICE OF BANDWIDTH FOR DENSITY-ESTIMATION [J].

FARAWAY, JJ ;

JHUN, MS .

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1990, 85 (412) :1119-1122

[6]

Hall P, 1996, J ROY STAT SOC B, V58, P361

[7] FORMULAS FOR MEAN INTEGRATED SQUARED ERROR OF NONLINEAR WAVELET-BASED DENSITY ESTIMATORS [J].

HALL, P ;

PATIL, P .

ANNALS OF STATISTICS, 1995, 23 (03) :905-928

[8]

Meyer Y., 2004, WAVELETS OPERATORS

[9]

NASON GP, 1995, WAVETHRESH VERSION 3

[10]

Wand MP., 1994, Kernel Smoothing

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