Extensions to Basu's theorem, factorizations, and infinite divisibility
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.''
scientific article; zbMATH DE number 5126461