Adaptive wavelet estimator for nonparametric density deconvolution

    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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