Extensions to Basu's theorem, factorizations, and infinite divisibility
type: Item
instance of: scholarly article
title: Extensions to Basu's theorem, factorizations, and infinite divisibility
zbMATH Open document ID: 1107.62003
author: Anirban DasGupta
published in: Journal of Statistical Planning and Inference
publication date: 2007-02-14T00:00:00Z
review text: From author's summary: ``We define a notion of approximate sufficiency and approximate ancillarity and show that such statistics are approximately independent pointwise under each value of the parameter. We do so without mentioning the somewhat non-intuitive concept of completeness, thus providing a more transparent version of Basu's theorem [see \textit{D. Basu}, Sankhyā 15, 377--380 (1955; Zbl 0068.13401)]. Two total variation inequalities are given, which we call approximate Basu theorems.'' There are interesting applications of the results obtained to the theory of infinitely divisible distributions. In particular, the author shows that Basu's theorem can be used to check infinite divisibility of some particular distributions. ``These applications indicate that the possible spectrum of applications of Basu's theorem is much broader than has been realized.''
Mathematics Subject Classification ID: 62B05
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 62F10
zbMATH DE Number: 5126461
zbMATH Keywords: ancillarity
zbMATH Keywords: completeness
zbMATH Keywords: Goldie-Steutel law
zbMATH Keywords: independence
zbMATH Keywords: sufficiency
zbMATH Keywords: total variation
reviewed by: Alexander Iksanov
MaRDI profile type: Publication
full work available at URL: j.jspi.2006.06.018
OpenAlex ID: W2097557492
Wikidata QID: Q114154312
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DOI: 10.1016/J.JSPI.2006.06.018
description: scientific article; zbMATH DE number 5126461