04:30 PM in CL50 Room 224
K. C. S. Pillai Memorial Lecture
Lawrence D. Brown, Professor of Mathematics and Director
of the Center of Statistics, Cornell University
Non-existence of Good Unbiased Estimators in Singular Problems
Abstract
In many nonparametric problems, such as density estimation,
nonparametric regression etc., all the existing good estimators are
biased (asymptotic or finite sample). There has long been a suspicion
that either good unbiased estimators do not exist for such problems
or they must be quite complicated. In this paper, we clarify the nonexistence
of good unbiased estimators in all singular problems both
for fixed sample size and asymptotically (this includes most problems
with optimal rate of convergence slower than n-4). We also discuss
situations in regular problems where such nonexistences can occur.
