Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 6 (2012), 91-122.
Non asymptotic minimax rates of testing in signal detection with heterogeneous variances
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.
Electron. J. Statist., Volume 6 (2012), 91-122.
First available in Project Euclid: 3 February 2012
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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