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Quadratic prediction problems in multivariate linear models

Author

Listed:
  • Liu, Xu-Qing
  • Wang, Dong-Dong
  • Rong, Jian-Ying

Abstract

Linear and quadratic prediction problems in finite populations have become of great interest to many authors recently. In the present paper, we mainly aim to extend the problem of quadratic prediction from a general linear model, of form , to a multivariate linear model, denoted by with . Firstly, the optimal invariant quadratic unbiased (OIQU) predictor and the optimal invariant quadratic (potentially) biased (OIQB) predictor of for any particular symmetric nonnegative definite matrix satisfying are derived. Secondly, we consider predicting and . The corresponding restricted OIQU predictor and restricted OIQB predictor for them are given. In addition, we also offer four concluding remarks. One concerns the generalization of predicting and , and the others are concerned with three possible extensions from multivariate linear models to growth curve models, to restricted multivariate linear models, and to matrix elliptical linear models.

Suggested Citation

  • Liu, Xu-Qing & Wang, Dong-Dong & Rong, Jian-Ying, 2009. "Quadratic prediction problems in multivariate linear models," Journal of Multivariate Analysis, Elsevier, vol. 100(2), pages 291-300, February.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:2:p:291-300
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    References listed on IDEAS

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    1. Liu, Xu-Qing & Rong, Jian-Ying, 2007. "Quadratic prediction problems in finite populations," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 483-489, March.
    2. Chaturvedi, Anoop & Wan, Alan T. K. & Singh, Shri P., 2002. "Improved Multivariate Prediction in a General Linear Model with an Unknown Error Covariance Matrix," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 166-182, October.
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    Cited by:

    1. Liu, Xu-Qing & Wang, Dong-Dong & Rong, Jian-Ying, 2009. "Quadratic prediction and quadratic sufficiency in finite populations," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1979-1988, October.

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