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| HAL : hal-00440825, version 2 |
| arXiv : 0912.2423 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (12-12-2009) | v2 (09-02-2010) |
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| Non asymptotic minimax rates of testing in signal detection with heterogeneous variances |
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| Béatrice Laurent 1Jean-Michel Loubès 1 |
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| (09/02/2010) |
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| 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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| 1 : | Institut de Mathématiques de Toulouse (IMT) |
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Université Paul Sabatier - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées de Toulouse – CNRS : UMR5219 |
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| Domaine | : | Mathématiques/Statistiques Statistiques/Théorie |
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| Goodness-of-fit tests – heterogeneous variances – inverse problems. |
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| hal-00440825, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00440825 | |
| oai:hal.archives-ouvertes.fr:hal-00440825 | |
| Contributeur : Clément Marteau | |
| Soumis le : Mardi 9 Février 2010, 10:31:32 | |
| Dernière modification le : Mardi 9 Février 2010, 10:33:54 | |
