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Unbiased estimation in the multivariate natural exponential family with simple quadratic variance function

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  • López Blázquez, Fernando
  • Gutiérrez Rubio, David

Abstract

We give expansions for the unbiased estimator of a parametric function of the mean vector in a multivariate natural exponential family with simple quadratic variance function. This expansion is given in terms of a system of multivariate orthogonal polynomials with respect to the density of the sample mean. We study some limit properties of the system of orthogonal polynomials. We show that these properties are useful to establish the limit distribution of unbiased estimators.

Suggested Citation

  • López Blázquez, Fernando & Gutiérrez Rubio, David, 2003. "Unbiased estimation in the multivariate natural exponential family with simple quadratic variance function," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 1-13, July.
    • Handle: RePEc:eee:jmvana:v:86:y:2003:i:1:p:1-13
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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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