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Complete and symmetrically complete families of distributions. (English) Zbl 0644.62011

The paper presents a variety of results of the type “completeness implies symmetric completeness”. Symmetric completeness of order k of a family of probability measures means that the family of k th powers of the probability measures is complete for the family of symmetric functions. The key tool is a polarization lemma which is proved in the appendix of the paper.
Reviewer: H.Strasser

MSC:

62E10 Characterization and structure theory of statistical distributions
62G05 Nonparametric estimation
62C07 Complete class results in statistical decision theory
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