Complete order statistics in parametric models

• 成果类型: Article
• 署名作者: Mattner, L
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 1265-1282
• 关键词: location families; distributions

摘要

For a given statistical model P it may happen that the order statistic is complete for each IID model based on 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 (X) over bar(n) is generically an optimal unbiased estimator, but, as it turns out, also generically asymptotically inefficient.