Ordered Smoothers With Exponential Weighting

Abstract: The main goal in this paper is to propose a new method for deriving oracle inequalities related to the exponential weighting method. For the sake of simplicity we focus on recovering an unknown vector from noisy data with the help of a family of ordered smoothers. The estimators withing this family are aggregated using the exponential weighting and the aim is to control the risk of the aggregated estimate. Based on simple probabilistic properties of the unbiased risk estimate, we derive new oracle inequalities and show that the exponential weighting permits to improve Kneip's oracle inequality.