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The linear minimax estimator of stochastic regression coefficients and parameters under quadratic loss function

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  • Yu, Sheng-Hua

Abstract

Consider stochastic effects linear model Y=X[beta]+[epsilon] with E([beta])=A[alpha],Cov([beta])=[sigma]2V1, E([epsilon])=0,Cov([epsilon])=[sigma]2V2, and E([beta][epsilon]')=0, where V1 and V2 are known positive definite matrices, [alpha][set membership, variant]Rk and [sigma]2>0 are unknown parameters. In this paper, we consider a particular quadratic loss function . On the basis of this we obtain the unique linear minimax estimator of the linear estimable function S[alpha]+Q[beta].

Suggested Citation

  • Yu, Sheng-Hua, 2007. "The linear minimax estimator of stochastic regression coefficients and parameters under quadratic loss function," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 54-62, January.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:1:p:54-62
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    Cited by:

    1. Liu, Xin & Yue, Rong-Xian & Chatterjee, Kashinath, 2014. "R-optimal designs in random coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 127-132.
    2. Hu, Guikai & Peng, Ping, 2012. "Matrix linear minimax estimators in a general multivariate linear model under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 286-295.

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