Résumé 273 :

Adaptive estimation over anisotropic functional classes
Lepski, Oleg
Université Aix-Marseille

We address the problem of adaptive minimax estimation in white gaussian noise model under L_p loss, on the anisotropic Nikolskii classes. We prove the existence of rate-adaptive estimators and fully characterize behavior of the minimax risk for different relationships between regularity parameters and norm indexes in definitions of the functional class and of the risk. In particular some new asymptotics of the minimax risk are discovered including necessary and sufficient conditions for existence a uniformly consistent estimator.