Open Access
January, 1977 Mixtures and Products of Dominated Experiments
Erik N. Torgersen
Ann. Statist. 5(1): 44-64 (January, 1977). DOI: 10.1214/aos/1176343739


It is shown, using a theorem of Choquet, that any separable experiment is a mixture of experiments admitting boundedly complete and sufficient statistics. The experiments possessing these properties are precisely the experiments which are extremal with respect to mixtures. Dominated models for independent observations $X_1, \cdots, X_n$ admitting boundedly (or $L_p$) complete and sufficient statistics, are considered. It is shown that a subset--say $X_1, \cdots, X_m$ where $m < n$--has the same property provided a regularity condition is satisfied. This condition is automatically satisfied when the observations are identically distributed. In the bounded complete case the proof uses the fact that products of experiments are distributive w.r.t. mixtures. More involved arguments are needed for $L_p$ completeness.


Download Citation

Erik N. Torgersen. "Mixtures and Products of Dominated Experiments." Ann. Statist. 5 (1) 44 - 64, January, 1977.


Published: January, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0365.62004
MathSciNet: MR438540
Digital Object Identifier: 10.1214/aos/1176343739

Primary: 62B15
Secondary: 62B05

Keywords: Extremal experiments , isometry criterion

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 1 • January, 1977
Back to Top