Partially complete sufficient statistics are jointly complete
Statistics Theory
2014-05-26 v2 Statistics Theory
Abstract
The theory of the basic statistical concept of (Lehmann-Scheff\'e-)completeness is perfected by providing the theorem indicated in the title and previously overlooked for several decades. Relations to earlier results are discussed and illustrating examples are presented. Of the two proofs offered for the main result, the first is direct and short, following the prototypical example of Landers and Rogge (1976), and the second is very short and purely statistical, utilizing the basic theory of optimal unbiased estimation in the little known version completed by Schmetterer and Strasser (1974).
Keywords
Cite
@article{arxiv.1307.3654,
title = {Partially complete sufficient statistics are jointly complete},
author = {Abram M. Kagan and Yaakov Malinovsky and Lutz Mattner},
journal= {arXiv preprint arXiv:1307.3654},
year = {2014}
}
Comments
16 pages. Very minor changes (one more reference, abstract slightly longer). To appear in Teoriya Veroyatnostei i ee Primeneniya