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Completeness of Order Statistics

Published online by Cambridge University Press:  20 November 2018

D. A. S. Fraser
D. A. S. Fraser*
Affiliation:
University of Toronto
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1. Introduction. Under the non-parametric assumption that a set of observations is a sample from an absolutely continuous distribution, the order statistics are known to form a complete sufficient statistic. It is proved in this note that it suffices to have the class of uniform distributions over finite numbers of intervals or the class of uniform distributions over sets of a ring which is a basis for the σ-algebra of Borel sets. This result is derived as a particular case of that of several samples from more general distributions.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 42 - 45
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Halmos, P., The range of a vector measure, Bull. Amer. Math. Soc, 54 (1948), 416–421.Google Scholar