Sufficiency and Exponential Families for Discrete Sample Spaces Export

@article{citeulike:1512305, abstract = {All known theorems of the Darmois-Koopman-Pitman type are based on the assumption of absolutely continuous probabilities. In this article, a Darmois-Koopman-Pitman type theorem is proved for families of probability measures that are defined on discrete sample spaces. Two assumptions are imposed on the sufficient statistic for the family: (1) the range space of the sufficient statistic can be completely ordered, and (2) this ordering of the range space of the sufficient statistic has a certain regularity property. Under (1) and (2), it can be proved that the given family is exponential of order 1.}, author = {Andersen, Erling B.}, citeulike-article-id = {1512305}, citeulike-linkout-0 = {http://www.jstor.org/stable/2284291}, journal = {Journal of the American Statistical Association}, keywords = {1d, discrete, exponential-families}, number = {331}, pages = {1248--1255}, posted-at = {2007-07-30 09:19:42}, priority = {2}, title = {Sufficiency and Exponential Families for Discrete Sample Spaces}, url = {http://www.jstor.org/stable/2284291}, volume = {65}, year = {1970} }

TY - JOUR ID - citeulike:1512305 L3 - citeulike-article-id:1512305 N2 - All known theorems of the Darmois-Koopman-Pitman type are based on the assumption of absolutely continuous probabilities. In this article, a Darmois-Koopman-Pitman type theorem is proved for families of probability measures that are defined on discrete sample spaces. Two assumptions are imposed on the sufficient statistic for the family: (1) the range space of the sufficient statistic can be completely ordered, and (2) this ordering of the range space of the sufficient statistic has a certain regularity property. Under (1) and (2), it can be proved that the given family is exponential of order 1. IS - 331 JF - Journal of the American Statistical Association EP - 1255 TI - Sufficiency and Exponential Families for Discrete Sample Spaces VL - 65 SP - 1248 KW - 1d KW - discrete KW - exponential-families AU - Andersen, Erling PY - 1970/// UR - http://www.jstor.org/stable/2284291 ER -