Tony Cai
Department of Statistics. The Wharton School.
University of Pennsylvania
On Optimal Estimation of A Nonsmooth Functional
In this talk I will discuss some recent work on optimal estimation of nonsmooth functionals.
These problems exhibit some interesting features that are significantly different from those
that occur in estimating conventional smooth functionals. This is a setting where standard
techniques fail. I will discuss a newly developed general minimax lower bound technique
that is based on testing two fuzzy hypotheses and illustrate the ideas by focusing on the
problem of optimal estimation of the l_1 norm of a high dimensional normal mean vector.
An estimator is constructed using approximation theory and Hermite polynomials and is shown
to be asymptotically sharp minimax. This is joint work with Mark Low.