Department of Statistics

Seminar

**Information Inequalities**

Andrew R. Barron

Professor of Statistics and Electrical Engineering

Yale University

The familiar Cramer-Rao inequality shows for unbiased estimators Y=g(X)

of a d-dimensional parameter vector a that the risk E[(Y-a) I(a) (Y-a)]

is never less than d, where I(a) is the Fisher information of p(x|a).

Moreover, an extension of this inequality due to Van Trees to deal
with

Bayes risk may be used to show that the minimax risk satisfies the
same

inequality. Here we take the analysis further to provide similar
lower

bounds for the Bayes risk with Hellinger or Kullback-Leibler loss in

estimating the density function p(.|a). Motivation for this work
comes

from predictive density estimation, data compression, and model selection.

*Seminar to be held in Room 107, 24 Hillhouse Avenue at 4:15 pm*