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The Annals of Statistics 2007, Vol. 35, No. 5, 22612286
 

Summary: The Annals of Statistics
2007, Vol. 35, No. 5, 22612286
DOI: 10.1214/009053607000000226
Institute of Mathematical Statistics, 2007
ON OPTIMALITY OF BAYESIAN TESTIMATION IN THE
NORMAL MEANS PROBLEM
BY FELIX ABRAMOVICH, VADIM GRINSHTEIN AND MARIANNA PENSKY1
Tel Aviv University, The Open University of Israel and
University of Central Florida
We consider a problem of recovering a high-dimensional vector ob-
served in white noise, where the unknown vector is assumed to be sparse.
The objective of the paper is to develop a Bayesian formalism which gives
rise to a family of l0-type penalties. The penalties are associated with various
choices of the prior distributions n() on the number of nonzero entries of
and, hence, are easy to interpret. The resulting Bayesian estimators lead to
a general thresholding rule which accommodates many of the known thresh-
olding and model selection procedures as particular cases corresponding to
specific choices of n(). Furthermore, they achieve optimality in a rather
general setting under very mild conditions on the prior. We also specify the
class of priors n() for which the resulting estimator is adaptively optimal

  

Source: Abramovich, Felix - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics