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A construction of the UMVU estimator for simple quadratic natural exponential families

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  • Pommeret, Denys

Abstract

This paper presents a construction of the uniformly minimum variance unbiased (UMVU) estimator of real-valued functions for the simple quadratic natural exponential families on . A polynomial expansion of the estimator is derived and a condition for its existence is given. The exact variance of the UMVU estimator is calculated. It is also shown that the series of the multidimensional Bhattacharyya bounds converges to this variance. These results are extensions of Morris (Ann. Statist. 11 (1983) 515) and Blight and Rao (Biometrika 61 (1974) 137). Some illustrations are indicated. Non-i.i.d. and biased cases are also discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:85:y:2003:i:2:p:217-233
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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.
    2. Pommeret, Denys, 1997. "Multidimensional Bhattacharyya Matrices and Exponential Families," Journal of Multivariate Analysis, Elsevier, vol. 63(1), pages 105-118, October.
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