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

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

2009-12-12

arxiv.org/abs/0912.2423v2

Mathematics

Statistics Theory

Scientific paper

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 $(Y_j)_{j\in J}$ of independent Gaussian random variables, having mean $(\theta_j)_{j\in J}$ and variance $(\sigma_j)_{j\in J}$. 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 $l_2$ and $l_{\infty}$ norms, without assumption on $(\sigma_j)_{j\in J}$ and on several functions spaces. Our point of view is completely non-asymptotic.

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