## The Annals of Statistics

### Complete order statistics in parametric models

L. Mattner

#### 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 in Project Euclid: 20 September 2002

http://projecteuclid.org/euclid.aos/1032526968

Digital Object Identifier
doi:10.1214/aos/1032526968

Mathematical Reviews number (MathSciNet)
MR1401849

Zentralblatt MATH identifier
0880.62009

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

#### Citation

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

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