Adaptive Wavelet Empirical Bayes Estimation Of A Location Or A Scale Parameter
62C12; 62G20; Adaptive estimation; Empirical Bayes estimation; Meyer-type wavelet; Posterior and prior risk
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.
Journal of Statistical Planning and Inference
Number of Pages
Source API URL
Pensky, Marianna, "Adaptive Wavelet Empirical Bayes Estimation Of A Location Or A Scale Parameter" (2000). Scopus Export 2000s. 771.