Abstract

This thesis deals with lower bounds for the minimax risk in general decision-theoretic problems. Such bounds are useful for assessing the quality of decision rules. After providing a unified treatment of existing techniques, we prove new lower bounds which involve f-divergences, a general class of dissimilarity measures between proba-bility measures. The proofs of our bounds rely on elementary convexity facts and are extremely simple. Special cases and straightforward corollaries of our results include many well-known lower bounds. As applications, we study a covariance matrix esti-mation problem and the problem of estimation of convex bodies from noisy support function measurements.