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Statistics
A Journal of Theoretical and Applied Statistics
Volume 45, 2011 - Issue 3
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Original Articles

Inference in ϕ-families of distributions

Pages 223-236 | Received 15 Mar 2008, Accepted 13 Oct 2009, Published online: 23 Feb 2010
 

Abstract

This paper is devoted to the study of the parametric family of multivariate distributions obtained by minimizing a convex functional under linear constraints. Under certain assumptions on the convex functional, it is established that this family admits an affine parameterization, and parametric estimation from an i.i.d. random sample is studied. It is also shown that the members of this family are the limit distributions arising in inference based on empirical likelihood. As a consequence, given a probability measure μ0 and an i.i.d. random sample drawn from μ0, nonparametric confidence domains on the generalized moments of μ0 are obtained.

AMS 2000 Classification :

Acknowledgements

The author is indebted to an anonymous referee for a very careful reading of the paper and insightful comments.

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