Universiteit Utrecht

Department of Mathematics

On an adaptive confidence set in white noise model

Eduard Belitser
(Utrecht University)

20 February 2007

In the context of adaptive nonparametric curve estimation problem, a common assumption is that a function (signal) to estimate belongs to a nested family of functional classes, parameterized by a quantity which often has a meaning of smoothness amount. It has already been realized by many that the problem of estimating the smoothness is not sensible. What can then be inferred about the smoothness? We attempt to answer this question. We consider the implications of our results to the  problem of adaptive estimation and construction of an "adaptive" confidence set. The procedure is based on the empirical Bayes approach (marginalized maximum likelihood estimator of the smoothness) for an appropriate prior distribution on the unknown signal.

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