A1203
Title: Minimax risk with random normalizing factors in the single-index model
Authors: Armel Fabrice Evrard Yode - Universite Felix Houphouet-Boigny (Cote d'Ivoire) [presenting]
Jean Philippe Nguessand Tchiekre - Ecole Nationale Superieure de Statistique et Economie Appliquees (Cote d'Ivoire)
Abstract: The nonparametric estimation problem of a multidimensional regression function is considered. The aim is to propose improvement in the optimal estimation rate from the minimax point of view. To avoid poor estimation quality or generally in models for which the minimax approach is unsatisfactory, a prior study introduced the concept of random normalizing factors in 1999. This concept is a combination of adaptive estimation and minimax hypothesis testing theory. This hybrid approach uses the results of test theory to consider adaptive estimation. So, via the concept of random normalizing factors introduced by the prior study, considering a plausible assumption that the regression function has a single-index structure, an estimator that can be adaptive is constructed and whose observation-dependent estimation rate is better than that obtained via the minimax approach, with prescribed confidence level n. In addition, the relevance of the results is demonstrated by applying them to real data sets.
