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Keywords:
mixed linear model; minimum norm quadratic estimation; variance components; first order fixed parameter unknowns; second order fixed parameter unknowns; invariant for translations
mixed linear model; minimum norm quadratic estimation; variance components; first order fixed parameter unknowns; second order fixed parameter unknowns; invariant for translations
Summary:
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 $D(\bold{Y)=0_1V_1 + ... + 0_mV_m}$.
References:
[1] J. Kleffe: Best quadratic unbiased estimators for variance components in mixed linear models. Sankhya, 38 (1976), 179-186. MR 0468051 | Zbl 0413.62052
[2] C. R. Rao: Estimation of variance and covariance components - MINQUE theory. Journ. Multivariant. Analysis, 1 (1971), 257-275. MR 0301869 | Zbl 0223.62086
[3] C. R. Rao K. S. Mitra: Generalized Inverse of Matrices and its Application. J. Wiley, N. York 1971. MR 0338013
[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 0849707 | Zbl 0605.62077
[6] Š. Varga: Estimations in Mixed Linear Models. Sborník VŠCHT Praha Řada M - Matematika, (1990), 1-10.
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