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

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  • Chacón, J.E.
  • Montanero, J.
  • Nogales, A.G.
  • Pérez, P.

Abstract

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].

Suggested Citation

  • Chacón, J.E. & Montanero, J. & Nogales, A.G. & Pérez, P., 2007. "Stability under products of sufficient, minimal sufficient and complete [sigma]-fields in the Bayesian case," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 710-716, April.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:7:p:710-716
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    1. Montanero, Jesús & Nogales, Agustín G. & Oyola, José A. & Pérez, Paloma, 2003. "Strong invariance under a Bayesian point of view," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 155-162, January.
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