SPEAKER: Vladimir Koltchinskii, Professor, Mathematics, Georgia Tech
TITLE: “Bias reduction and efficiency in estimation of smooth functionals of high-dimensional parameters”
ABSTRACT: We will discuss a problem of estimation of smooth functionals of high-dimensional parameters of statistical models. The main focus will be on a method of bias reduction based on approximate solutions of integral equations on the parameter space with respect to certain Markov kernels.
In the case of high-dimensional normal models, this approach yields estimators with optimal or nearly optimal mean squared error rates (in particular, asymptotically efficient estimators) for all sufficiently smooth functionals. The proofs of these results rely on a variety of tools including Gaussian concentration, representations of Markov chains as superpositions of smooth random maps and information-theoretic lower bounds.
DATE: Thursday, February 6th, 4:10pm
LOCATION: MSB 1147, Colloquium Room
REFRESHMENTS at 3:30pm in MSB 4110 (4th floor lounge)