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December 1999 Adaptive wavelet estimator for nonparametric density deconvolution
Marianna Pensky, Brani Vidakovic
Ann. Statist. 27(6): 2033-2053 (December 1999). DOI: 10.1214/aos/1017939249

Abstract

The problem of estimating a density $g$ based on a sample $X_1, X_2,\dots, X_n$ from $p = q*g$ is considered. Linear and nonlinear wavelet estimators based 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.

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Marianna Pensky. Brani Vidakovic. "Adaptive wavelet estimator for nonparametric density deconvolution." Ann. Statist. 27 (6) 2033 - 2053, December 1999. https://doi.org/10.1214/aos/1017939249

Information

Published: December 1999
First available in Project Euclid: 4 April 2002

zbMATH: 0962.62030
MathSciNet: MR1765627
Digital Object Identifier: 10.1214/aos/1017939249

Subjects:
Primary: 62G05
Secondary: 62G07

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 6 • December 1999
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