Geodesic
Quadratic estimations in mixed linear models
Applications of Mathematics, Tome 36 (1991) no. 2, pp. 134-144

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MR Zbl
In the paper four types of estimations of the linear function of the variance components are presented for the mixed linear model $\bold{Y=X \beta + e}$ with expectation $E(\bold{Y)=X \beta}$ and covariance matrix $D(\bold{Y)=0_1V_1 + ... + 0_mV_m}$.
In the paper four types of estimations of the linear function of the variance components are presented for the mixed linear model $\bold{Y=X \beta + e}$ with expectation $E(\bold{Y)=X \beta}$ and covariance matrix $D(\bold{Y)=0_1V_1 + ... + 0_mV_m}$.
DOI : 10.21136/AM.1991.104450
Classification : 62F10, 62J10, 62J99
Keywords: mixed linear model; minimum norm quadratic estimation; variance components; first order fixed parameter unknowns; second order fixed parameter unknowns; invariant for translations 
Varga, Štefan. Quadratic estimations in mixed linear models. Applications of Mathematics, Tome 36 (1991) no. 2, pp. 134-144. doi: 10.21136/AM.1991.104450
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     zbl = {0742.62074},
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     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1991.104450/}
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[1] J. Kleffe: Best quadratic unbiased estimators for variance components in mixed linear models. Sankhya, 38 (1976), 179-186. | MR | Zbl

[2] C. R. Rao: Estimation of variance and covariance components - MINQUE theory. Journ. Multivariant. Analysis, 1 (1971), 257-275. | MR | Zbl

[3] C. R. Rao K. S. Mitra: Generalized Inverse of Matrices and its Application. J. Wiley, N. York 1971. | MR

[4] C. R. Rao J. Kleffe: Estimation of Variance Components. In: P. R. Krisnaiah, ed. Handbook of Statistics, Vol. I. North Holland, N. York, (1980), 1-40.

[5] Š. Varga: Minimum Variance Quadratic Unbiased Estimation of Variance Components. Math. Slovaca, 36 No. 2 (1986), 163-170. | MR | Zbl

[6] Š. Varga: Estimations in Mixed Linear Models. Sborník VŠCHT Praha Řada M - Matematika, (1990), 1-10.

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