Title

Adaptive Wavelet Empirical Bayes Estimation Of A Location Or A Scale Parameter

Keywords

62C12; 62G20; Adaptive estimation; Empirical Bayes estimation; Meyer-type wavelet; Posterior and prior risk

Abstract

Assume that in independent two-dimensional random vectors (X1,θ1),...,(Xn,θn), each θi is distributed according to some unknown prior density function g. Also, given θi=θ,Xi has the conditional density function q(x-θ),x,θ∈(-∞,∞) (a location parameter case), or θ-1q(x/θ),x,θ∈(0,∞) (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,θn+1) is obtained, the objective is to construct an empirical Bayes (EB) estimator of θ. In this paper we derive the EB estimators of θ 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 Hα with an unknown α, but also when g is supersmooth. © 2000 Elsevier Science B.V.

Publication Date

10-1-2000

Publication Title

Journal of Statistical Planning and Inference

Volume

90

Issue

2

Number of Pages

275-292

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/s0378-3758(00)00123-3

Socpus ID

0042207174 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0042207174

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