Abstract
The aim of this paper is to establish non-asymptotic minimax rates for goodness-of-fit hypotheses testing in an heteroscedastic setting. More precisely, we deal with sequences (Yj)j∈J of independent Gaussian random variables, having mean (θj)j∈J and variance (σj)j∈J. The set J will be either finite or countable. In particular, such a model covers the inverse problem setting where few results in test theory have been obtained. The rates of testing are obtained with respect to l2 norm, without assumption on (σj)j∈J and on several functions spaces. Our point of view is entirely non-asymptotic.
Citation
Béatrice Laurent. Jean-Michel Loubes. Clément Marteau. "Non asymptotic minimax rates of testing in signal detection with heterogeneous variances." Electron. J. Statist. 6 91 - 122, 2012. https://doi.org/10.1214/12-EJS667
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