Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 2, pp. 214-231

EMPIRICAL BAYES ESTIMATION BASED ON WAVELETS

By

M. PENSKY, University of Central Florida, Orlando
BRENDA MACGIBBON, Université du Québec à Montréal, Montréal
SHUPEI WANG, Hôpital Ste-Justine, Montréal

SUMMARY. Empirical Bayes estimators are constructed via wavelet approximation. Posterior and prior risks of the estimators are investigated and the convergence rates are derived. Examples demonstrate Bayes estimation estimation of q when the conditional density belongs to a one-parameter exponential family and empirical Bayes estimation of qt, t>0, for the uniform conditional density.

AMS (1991) subject classification.Primary 62C12, secondary 62G20.

Key words and phrases. Empirical Bayes estimation, multiresolution analysis, wavelet, posterior and prior risk.

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