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SUMMARY:Adaptation in some shape-constrained regression problems - Adityan
 and Guntuboyina\, University of California\, Berkeley\,
DTSTART:20140623T154500Z
DTEND:20140623T161500Z
UID:TALK53100@talks.cam.ac.uk
CONTACT:37296
DESCRIPTION:We consider the problem of estimating a normal mean constraine
 d to be in a convex\npolyhedral cone in Euclidean space. We say that the t
 rue mean is sparse if it\nbelongs to a low dimensional face of the cone. W
 e show that\, in a certain natural\nsubclass of these problems\, the maxim
 um likelihood estimator automatically adapts\nto sparsity in the underlyin
 g true mean. We discuss the problems of convex\nregression and univariate 
 and bivariate isotonic regression as examples.
LOCATION:Centre for Mathematical Sciences\, Meeting Room 2
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