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

Fernando López Blázquez and David Gutiérrez Rubio
Authors registered in the RePEc Author Service: Fernando López-Blázquez

Journal of Multivariate Analysis, 2003, vol. 86, issue 1, 1-13

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.

Keywords: Exponential; families; Orthogonal; polynomials; Multivariate; Hermite; polynomials; Orthogonal; expansions; Limit; distributions (search for similar items in EconPapers)
Date: 2003
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