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Nonnegative Minimum Biased Quadratic Estimation in the Linear Regression Models

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  • Gnot, S.
  • Trenkler, G.
  • Zmyslony, R.

Abstract

In the paper the problem of nonnegative estimation of [beta]'H[beta] + h[sigma]2 in the linear model E(y) = X[beta], Var(y)= [sigma]2I is discussed. Here H is a nonnegative definite matrix while h is a nonnegative scalar. An iterative procedure for the nonnegative minimum biased quadratic estimator is described. Moreover, in the case that H and X'X commute, an explicit formula for this estimator is given. Admissibility of the estimator is proved. The results are applied to nonnegative estimation of the total mean squared error of a linear biased estimator.

Suggested Citation

  • Gnot, S. & Trenkler, G. & Zmyslony, R., 1995. "Nonnegative Minimum Biased Quadratic Estimation in the Linear Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 54(1), pages 113-125, July.
    • Handle: RePEc:eee:jmvana:v:54:y:1995:i:1:p:113-125
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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.
    2. Housila Singh & Sushil Shukla, 2003. "A family of shrinkage estimators for the square of mean in normal distribution," Statistical Papers, Springer, vol. 44(3), pages 433-442, July.

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