Signal detection for inverse problems in a multidimensional framework

Yuri I. Ingster (1, 2) , Béatrice Laurent (3, 4) , Clément Marteau (3)

1 St. Petersburg State Electrotechnical University
2 LETI - Saint Petersburg Electrotechnical University
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 INSA Toulouse - Institut National des Sciences Appliquées - Toulouse

This paper is devoted to multi-dimensional inverse problems. In this setting, we address a goodness-of-fit testing problem. We investigate the separation rates associated to different kinds of smoothness assumptions and different degrees of ill-posedness.

Mots clés: Inverse problems; Tests; Signal detection

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Yuri I. Ingster, Béatrice Laurent, Clément Marteau. Signal detection for inverse problems in a multidimensional framework. Mathematical Methods of Statistics, 2014, 23 (4), pp.279-305. ⟨10.3103/S1066530714040036⟩. ⟨hal-00949479⟩