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Multidimensional Bhattacharyya Matrices and Exponential Families

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  • Pommeret, Denys

Abstract

Shanbhag (1972, 1979) has characterized the distributions belonging to an exponential family on such that the Bhattacharyya matrix is diagonal. Since then, this set of distributions has been classed by Morris (1982) and is referred to as the class of quadratic natural exponential families. In this paper we consider a multidimensional extension of Shanbhag and we obtain a characterization of the quadratic natural exponential families on d.

Suggested Citation

  • Pommeret, Denys, 1997. "Multidimensional Bhattacharyya Matrices and Exponential Families," Journal of Multivariate Analysis, Elsevier, vol. 63(1), pages 105-118, October.
    • Handle: RePEc:eee:jmvana:v:63:y:1997:i:1:p:105-118
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    References listed on IDEAS

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    1. D. Pommeret, 1996. "Orthogonal polynomials and natural exponential families," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 5(1), pages 77-111, June.
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    Cited by:

    1. Pommeret, Denys, 2003. "A construction of the UMVU estimator for simple quadratic natural exponential families," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 217-233, May.

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