کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1150674 | 957971 | 2007 | 8 صفحه PDF | دانلود رایگان |
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 nonintuitive concept of completeness, thus providing a more transparent version of Basu's theorem. Two total variation inequalities are given, which we call approximate Basu theorems.We also show some new types of applications of Basu's theorem in the theory of probability. The applications are to showing that large classes of random variables are infinitely divisible (id), and that others admit a decomposition in the form YZ, where Y is infinitely divisible, Z is not, both are nondegenerate, and Y and Z are independent.These applications indicate that the possible spectrum of applications of Basu's theorem is much broader than has been realized.
Journal: Journal of Statistical Planning and Inference - Volume 137, Issue 3, 1 March 2007, Pages 945–952