Adaptive wavelet empirical Bayes estimation of a location or a scale parameter

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    Keywords

    empirical Bayes estimation; adaptive estimation; Meyer-type wavelet; posterior and prior risk; DENSITY-ESTIMATION; CURVE ESTIMATION; RATES; CONVERGENCE; ERROR; Statistics & Probability

    Abstract

    Assume that in independent two-dimensional random vectors (X-1, theta(1)),..., (X-n, theta(n)), each theta(i) is distributed according to some unknown prior density function g. Also, given theta(i) = theta, X-i has the conditional density function q(x - theta), x, theta is an element of (-infinity, infinity) (a location parameter case), or 0(-1) q(x/0), x, 0 is an element of (0, infinity) (a scale parameter case). In each pair the first component is observable, but the second is not. After the (n+1)th pair (Xn+1, theta(n+1)) is obtained, the objective is to construct an empirical Bayes (EB) estimator of 0. In this paper we derive the EB estimators of theta based on a wavelet approximation with Meyer-type wavelets. We show that these estimators provide adaptation not only in the case when g belongs to the Sobolev space H-alpha with an unknown alpha, but also when g is supersmooth. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 62C12; 62G20.

    Journal Title

    Journal of Statistical Planning and Inference

    Volume

    90

    Issue/Number

    2

    Publication Date

    1-1-2000

    Document Type

    Article

    Language

    English

    First Page

    275

    Last Page

    292

    WOS Identifier

    WOS:000089364600007

    ISSN

    0378-3758

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