K.C.S.Pillai Memorial Lecture

Non-existence of Good Unbiased Estimators in Singular Problems

Lawrence D. Brown
Professor of Mathematics and Director of the Center of Statistics
Indian Statistical InstituteCornell University

Start Date and Time: Wed, 24 Apr 1991, 4:30 PM

End Date and Time: Wed, 24 Apr 1991, 5:30 PM

Venue: CL50 Room 224

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.

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