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Quadratic prediction problems in finite populations

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  • Liu, Xu-Qing
  • Rong, Jian-Ying

Abstract

In this paper, we investigate quadratic prediction problems of f(Y)=Y'HY with H satisfying HX=0 in finite populations under the linear model Y=X[beta]+e, . We mainly aim at proposing two notions of optimal invariant quadratic unbiased predictor and optimal invariant quadratic (potentially) biased predictor, and studying the structure of their explicit representations. In addition, we apply the main results of this paper to some special cases and finally derive a conclusion, which is not only mathematically interesting but also practically significant.

Suggested Citation

  • Liu, Xu-Qing & Rong, Jian-Ying, 2007. "Quadratic prediction problems in finite populations," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 483-489, March.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:5:p:483-489
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    References listed on IDEAS

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    1. 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. Xu, Li-Wen & Yu, Sheng-Hua, 2012. "Admissible prediction in superpopulation models with random regression coefficients under matrix loss function," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 68-76, January.
    2. 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.
    3. 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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