## The Annals of Statistics

### Adaptive wavelet estimator for nonparametric density deconvolution

#### 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.

#### Article information

Source
Ann. Statist. Volume 27, Number 6 (1999), 2033-2053.

Dates
First available in Project Euclid: 4 April 2002

http://projecteuclid.org/euclid.aos/1017939249

Digital Object Identifier
doi:10.1214/aos/1017939249

Mathematical Reviews number (MathSciNet)
MR1765627

Zentralblatt MATH identifier
0962.62030

Subjects
Primary: 62G05: Estimation
Secondary: 62G07: Density estimation

#### Citation

Pensky, Marianna; Vidakovic, Brani. Adaptive wavelet estimator for nonparametric density deconvolution. Ann. Statist. 27 (1999), no. 6, 2033--2053. doi:10.1214/aos/1017939249. http://projecteuclid.org/euclid.aos/1017939249.

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