COMPLETE ORDER-STATISTICS IN PARAMETRIC MODELS

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 rele vant results for large nonparametric models and pointing out generaliz ations to small nonparametric models, we essentially prove that this h appens generically even in smooth parametric models. As a consequence it may be argued that any statistic depending symmetrically on the obs ervations can be regarded as an optimal unbiased estimator of its expe ctation. In particular, the sample mean (X) over bar(n) is generically an optimal unbiased estimator, but, as it turns out, also generically asymptotically inefficient.