Using a locally Lipschitz function $T$ of $n > 1$ variables one can reduce data consisting of a sample of size $n$ to one real number. If we are given a family of probability measures on the real line which are equivalent to Lebesgue measure then $T$ yields a sufficient data reduction only if the given family is exponential. This result is compared with the results of Brown (1964) and Denny (1970).
Publié le : 1974-11-14
Classification:
Sufficient statistic characterization of exponential families,
62B05,
62E10,
39A40
@article{1176342879,
author = {Hipp, Christian},
title = {Sufficient Statistics and Exponential Families},
journal = {Ann. Statist.},
volume = {2},
number = {1},
year = {1974},
pages = { 1283-1292},
language = {en},
url = {http://dml.mathdoc.fr/item/1176342879}
}
Hipp, Christian. Sufficient Statistics and Exponential Families. Ann. Statist., Tome 2 (1974) no. 1, pp. 1283-1292. http://gdmltest.u-ga.fr/item/1176342879/