Open Access
June 1996 Complete order statistics in parametric models
L. Mattner
Ann. Statist. 24(3): 1265-1282 (June 1996). DOI: 10.1214/aos/1032526968


For a given statistical model $\mathsf{P}$ it may happen that the order statistic is complete for each IID model based on $\mathsf{P}$. After reviewing known relevant results for large nonparametric models and pointing out generalizations to small nonparametric models, we essentially prove that this happens generically even in smooth parametric models.

As a consequence it may be argued that any statistic depending symmetrically on the observations can be regarded as an optimal unbiased estimator of its expectation.

In particular, the sample mean $\overline{X}_n$ is generically an optimal unbiased estimator, but, as it turns out, also generically asymptotically inefficient.


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L. Mattner. "Complete order statistics in parametric models." Ann. Statist. 24 (3) 1265 - 1282, June 1996.


Published: June 1996
First available in Project Euclid: 20 September 2002

zbMATH: 0880.62009
MathSciNet: MR1401849
Digital Object Identifier: 10.1214/aos/1032526968

Primary: 62B05 , 62F10

Keywords: Asymptotic efficiency , contamination model , IID model , minimal sufficiency , nonparametric neighborhoods , optimal unbiased estimation , symmetrical completeness , UMVU , Unimodality

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 3 • June 1996
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