Complete order statistics in parametric models

Mattner, L.

Ann. Statist., Tome 24 (1996) no. 6, p. 1265-1282 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 1996-06-14
Classification:  Asymptotic efficiency,  contamination model,  IID model,  minimal sufficiency,  nonparametric neighborhoods,  optimal unbiased estimation,  symmetrical completeness,  UMVU,  unimodality,  62B05,  62F10