PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Empirical Bayesian Test of the Smoothness
Eduard Belitser and Farida Enikeeva
Eurandom Technical Report Volume 2005-014, 2005.

Abstract

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 then can be inferred about the smoothness? The paper attempts to answer this question. We consider the implications of our results to hypothesis testing. We also relate them to the problem of adaptive estimation. The test statistic is based on the marginalized maximum likelihood estimator of the smoothness for an appropriate prior distribution on the unknown signal.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:702
Deposited By:Farida Enikeeva
Deposited On:28 November 2005