The Annals of Statistics

Complete order statistics in parametric models

L. Mattner

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist. Volume 24, Number 3 (1996), 1265-1282.

Dates
First available: 20 September 2002

Permanent link to this document
http://projecteuclid.org/euclid.aos/1032526968

Mathematical Reviews number (MathSciNet)
MR1401849

Digital Object Identifier
doi:10.1214/aos/1032526968

Zentralblatt MATH identifier
0880.62009

Subjects
Primary: 62B05: Sufficient statistics and fields 62F10: Point estimation

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

Citation

Mattner, L. Complete order statistics in parametric models. The Annals of Statistics 24 (1996), no. 3, 1265--1282. doi:10.1214/aos/1032526968. http://projecteuclid.org/euclid.aos/1032526968.


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