In this paper we study the problem of adaptive estimation of a multivariate function satisfying some structural assumption. We propose a novel estimation procedure that adapts simultaneously to unknown structure and smoothness of the underlying function. The problem of structural adaptation is stated as the problem of selection from a given collection of estimators. We develop a general selection rule and establish for it global oracle inequalities under arbitrary double-struck Lp-losses. These results are applied for adaptive estimation in the additive multi-index model.
Bibliographical noteFunding Information:
Supported by the ISF grant No. 389/07.
- Adaptive estimation
- Minimax risk
- Optimal rates of convergence
- Oracle inequalities
- Structural adaptation
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty