Localized Upper and Lower Bounds for Some Estimation Problems

Abstract. We derive upper and lower bounds for some statistical estimation problems. The upper bounds are established for the Gibbs algorithm. The lower bounds, applicable for all statistical estimators, match the obtained upper bounds for various problems. Moreover, our framework can be regarded as a natural generalization of the standard minimax framework, in that we allow the performance of the estimator to vary for different possible underlying distributions according to a pre-defined prior.

• Type: Conference
• Year: 2005
• Where: COLT
• Authors: Tong Zhang
• Keywords: COLT 2005, Lower Bounds, Obtained Upper Bounds, Upper Bounds