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Nonnegative Minimum Biased Quadratic Estimation in Mixed Linear Models

Author

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  • Gnot, Stanislaw
  • Grzadziel, Mariusz

Abstract

The problem of nonnegative quadratic estimation of a parametric function [gamma]([beta], [sigma])=[beta]'F[beta]+[summation operator]ri=1 fi[sigma]2i in a general mixed linear model {y, X[beta], V([sigma])=[summation operator]ri=1 [sigma]2iVi} is discussed. Necessary and sufficient conditions are given for y'A0y to be a minimum biased estimator for [gamma]. It is shown how to formulate the problem of finding a nonnegative minimium biased estimator of [gamma] as a conic optimization problem, which can be efficiently solved using convex optimization techniques. Models with two variance components are considered in detail. Some applications to one-way classification mixed models are given. For these models minimum biased estimators with minimum norms for square of expectation [beta]2 and for [sigma]21 are presented in explicit forms.

Suggested Citation

  • Gnot, Stanislaw & Grzadziel, Mariusz, 2002. "Nonnegative Minimum Biased Quadratic Estimation in Mixed Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 217-233, February.
  • Handle: RePEc:eee:jmvana:v:80:y:2002:i:2:p:217-233
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    References listed on IDEAS

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    1. Norbert Gaffke & Rudolf Mathar, 1989. "A cyclic projection algorithm via duality," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 36(1), pages 29-54, December.
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    Cited by:

    1. Liu, Xu-qing & Rong, Jian-ying, 2007. "Nonnegative quadratic estimation and quadratic sufficiency in general linear models," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1180-1194, July.

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