Electronic Journal of Statistics

Non asymptotic minimax rates of testing in signal detection with heterogeneous variances

Béatrice Laurent, Jean-Michel Loubes, and Clément Marteau

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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)jJ of independent Gaussian random variables, having mean (θj)jJ and variance (σj)jJ. 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)jJ and on several functions spaces. Our point of view is entirely non-asymptotic.

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Electron. J. Statist., Volume 6 (2012), 91-122.

First available in Project Euclid: 3 February 2012

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Zentralblatt MATH identifier

Primary: 62G05: Estimation 62K20: Response surface designs

Goodness-of-fit tests heterogeneous variances inverse problems


Laurent, Béatrice; Loubes, Jean-Michel; Marteau, Clément. Non asymptotic minimax rates of testing in signal detection with heterogeneous variances. Electron. J. Statist. 6 (2012), 91--122. doi:10.1214/12-EJS667. https://projecteuclid.org/euclid.ejs/1328280899

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