Abstract
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).
Citation
Christian Hipp. "Sufficient Statistics and Exponential Families." Ann. Statist. 2 (6) 1283 - 1292, November, 1974. https://doi.org/10.1214/aos/1176342879
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