Generalization of the Fisher-Darmois-Koopman-Pitman Theorem on Sufficient Statistics

The well-known and now classical theorem (or, rather, theorems) referred to in the title shows that, for a family of n-dimensional densities of product form, with identical 1-dimensional factor densities, the existence of a sufficient statistic of dimension < n is essentially equivalent to the co...

Full description

Saved in:
Bibliographic Details
Published in:Sankhya. Series A 1963-09, Vol.25 (3), p.217-244
Main Authors: Barankin, Edward W., Maitra, Ashok P.
Format: Article
Language:English
Subjects:
Analyticity
Analytics
Factorization
Integers
Mathematical constants
Mathematical functions
Necessary conditions
Statistical theories
Statistics
Sufficient conditions
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The well-known and now classical theorem (or, rather, theorems) referred to in the title shows that, for a family of n-dimensional densities of product form, with identical 1-dimensional factor densities, the existence of a sufficient statistic of dimension < n is essentially equivalent to the condition that the 1-dimensional factor density involved be of exponential type (see below for more precise descriptions). In this article we drop the feature that the factor densities be identical, and we obtain theorems again relating the existence of lower dimensional sufficient statistics with the fact of exponential type for the factor densities. Results of the classical type fall out as corollaries.
ISSN:0581-572X