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Minimum variance quadratic unbiased estimation of variance components. (English) Zbl 0605.62077

An estimator of a function of the variance components of a random vector Y with covariance matrix \(D(Y)=\theta_ 1V_ 1+...+\theta_ mV_ m\) is given in the form Y’A(S)Y, where the matrix S contains prior values of elements of D(Y).

MSC:

62J10 Analysis of variance and covariance (ANOVA)
62H12 Estimation in multivariate analysis
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References:

[1] KLEFFE J.: Best quadratic unbiased estimators for variance components in mixed linear models. Sankhya 38. 1976, 179-186. · Zbl 0413.62052
[2] RAO C. R.: Estimation of variance and covariance components-MINQUE theory. Journ. Multivariat. Analysis 1, 1971, 257-275. · Zbl 0223.62086 · doi:10.1016/0047-259X(71)90001-7
[3] RAO C. R., MITRA K. S.: Generalized Inverse of Matrices and its Application. J. Wiley, N. York 1971. · Zbl 0236.15004
[4] RAO. C. R., KLEFFE J.: Estimation of Variance Components. Krisnaiah, P. R. Handbook of Statistics, Vol. I. 1-40, North Holland, N. York 1980. · Zbl 0476.62058
[5] SEELY J.: Linear spaces and unbiased estimation-application to the mixed linear model. Ann. Math. Statistics, 41, 1970, 1735-1748. · Zbl 0263.62041 · doi:10.1214/aoms/1177696818
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