Stability under products of sufficient, minimal sufficient and complete [sigma]-fields in the Bayesian case

• Published in: Statistics & probability letters Vol. 77; no. 7; pp. 710 - 716
• Main Authors: Nogales, A.G, Pérez, P, Montanero, J, Chacón, J.E
• Format: Journal Article
• Language: English
• Published: Elsevier 01.04.2007
• Series: Statistics & Probability Letters
• Subjects: Minimal sufficiency Invariance Completeness Identification
• ISSN: 0167-7152; 1879-2103
• DOI: 10.1016/j.spl.2006.11.015

In this paper, we present some Bayesian results about the stability under products of the concepts of sufficiency, minimal sufficiency and completeness, extending frequentist results by Chacón et al. [2006. A note on minimal sufficiency. Statist. Sinica 16 (1), 7-14] and Landers and Rogge [1976. A note on completeness, Scand. J. Statist. 3, 139]. These results are used to throw some light on the study of the relationship between minimal sufficiency and invariance, a question that, in a classical setting, has been considered in the first of the former papers and in Hall et al. [1965. The relationship between sufficiency and invariance with applications in sequential analysis. Ann. Math. Statist. 36, 575-614].