Sufficient Statistics and Discrete Exponential Families
Denny, J. L.
Ann. Math. Statist., Tome 43 (1972) no. 6, p. 1320-1322 / Harvested from Project Euclid
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$\{P_\theta\}$ is a set of probabilities on a countable set $_\chi$ such that $P_\theta(x) > 0$ for each $x$ and $\theta$. We prove that if $\{P_\theta\}$ is not an exponential family, then each sufficient statistic for $n$ independent observations must be one-to-one, modulo permutations, on an infinite product set (which does not depend on the sufficient statistic).
Publié le : 1972-08-14
Classification:  
@article{1177692483,
     author = {Denny, J. L.},
     title = {Sufficient Statistics and Discrete Exponential Families},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 1320-1322},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177692483}
}

Denny, J. L. Sufficient Statistics and Discrete Exponential Families. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  1320-1322. http://gdmltest.u-ga.fr/item/1177692483/