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

2009/12/12 by Béatrice Laurent, Laurent, Béatrice, Jean-Michel Loubès +3 · 1 citation
Mathematics · #62G05 #62G20 #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:62G05 #msc:62G20 #stat.TH

paper · pdf · doi:10.48550/arxiv.0912.2423

arxiv created 2010/02/09 · arxiv updated 2010/02/26

Abstract

The aim of this paper is to establish non-asymptotic minimax rates of testing for goodness-of-fit hypotheses in a heteroscedastic setting. More precisely, we deal with sequences (Y_j)_{j∈ J} of independent Gaussian random variables, having mean (θ_j)_{j∈ J} and variance (σ_j)_{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 and l_∞ norms, without assumption on (σ_j)_{j∈ J} and on several functions spaces. Our point of view is completely non-asymptotic.

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