Statistics Papers

Document Type

Journal Article

Date of this Version

1993

Publication Source

The Annals of Statistics

Volume

21

Issue

1

Start Page

1

Last Page

13

DOI

10.1214/aos/1176349012

Abstract

In many nonparametric problems, such as density estimation, nonparametric regression and so on, all the existing informative estimators are biased (asymptotic or finite sample). There has long been a suspicion that either informative unbiased estimators do not exist for such problems or they must be quite complicated. In this paper, we clarify the nonexistence of informative 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−1/2). We also discuss situations in regular problems where such nonexistences can occur.

Keywords

unbiasedness, modulus of continuity, Hellinger distance, singular problems

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Date Posted: 27 November 2017

This document has been peer reviewed.