Title

Adaptive wavelet estimator for nonparametric density deconvolution

Authors

Authors

M. Pensky;B. Vidakovic

Comments

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Abbreviated Journal Title

Ann. Stat.

Keywords

mixing distribution; wavelet transformation; Sobolev space; Meyer; wavelet; MULTIVARIATE DENSITIES; ASYMPTOTIC NORMALITY; STATIONARY-PROCESSES; CURVE ESTIMATION; OPTIMAL RATES; CONVERGENCE; KERNEL; ERROR; Statistics & Probability

Abstract

The problem of estimating a density g based on a sample X-1, X-2, X-n from p = q * g is considered. Linear and nonlinear wavelet estimators teased on Meyer-type wavelets are constructed. The estimators are asymptotically optimal and adaptive if g belongs to the Sobolev space H-alpha. Moreover, the estimators considered in this paper adjust automatically to the situation when g is supersmooth.

Journal Title

Annals of Statistics

Volume

27

Issue/Number

6

Publication Date

1-1-1999

Document Type

Article

Language

English

First Page

2033

Last Page

2053

WOS Identifier

WOS:000087132100011

ISSN

0090-5364

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