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March, 1993 Nonexistence of Informative Unbiased Estimators in Singular Problems
Richard C. Liu, Lawrence D. Brown
Ann. Statist. 21(1): 1-13 (March, 1993). 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.

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Richard C. Liu. Lawrence D. Brown. "Nonexistence of Informative Unbiased Estimators in Singular Problems." Ann. Statist. 21 (1) 1 - 13, March, 1993. https://doi.org/10.1214/aos/1176349012

Information

Published: March, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0783.62026
MathSciNet: MR1212163
Digital Object Identifier: 10.1214/aos/1176349012

Subjects:
Primary: 62F11
Secondary: 62A99, 62F12, 62G05

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 1 • March, 1993
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