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Conditional natural exponential families

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  • Masmoudi, Afif

Abstract

Let F={P[theta];[theta][set membership, variant][Theta]} be a natural exponential family on and let H be an exposed face of the closed convex hull of the F support. The aim of this paper is to study the asymptotic behavior of the law P[theta]+[lambda]u as [lambda] increases to +[infinity], for all u exterior normal vector of H. We obtain a degenerate weak limit P[theta],+[infinity] concentrated on the face H. The relation between the conditional law of P[theta] given H and P[theta],+[infinity] is established and some illustrating examples are given.

Suggested Citation

  • Masmoudi, Afif, 2006. "Conditional natural exponential families," Statistics & Probability Letters, Elsevier, vol. 76(17), pages 1882-1888, November.
  • Handle: RePEc:eee:stapro:v:76:y:2006:i:17:p:1882-1888
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    Cited by:

    1. Louati, Mahdi, 2013. "Mixture and reciprocity of exponential models," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 452-458.

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