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

Mandelbaum, Avi; Rüschendorf, Ludger

Ann. Stat. 15, 1229-1244 (1987).

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

Keywords:

completeness of generalized order statistics; unbiased estimation; tensor products of Hilbert spaces; completeness implies symmetric completeness; symmetric functions; polarization