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Keywords:
risk function; explicit expression; Bayes invariant quadratic unbiased estimate; linear function of the variance components; mixed linar model; normal case
risk function; explicit expression; Bayes invariant quadratic unbiased estimate; linear function of the variance components; mixed linar model; normal case
Summary:
In the paper an explicit expression for the Bayes invariant quadratic unbiased estimate of the linear function of the variance components is presented for the mixed linear model $\bold{t=X\beta+\epsilon}$, $\bold{E(t)=X\beta}$, $\bold{D(t)=0_1U_1+0_2U_2}$ with the unknown variance componets in the normal case. The matrices $\bold{U_1}$, $\bold{U_2}$ may be singular. Applications to two examples of the analysis of variance are given.
References:
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[2] L. Kubáček: Fundaments of the theory of estimates. (Slovak). Veda, Publishing House of Slovak Acad. Sc., Bratislava 1983,.
[3] C. R. Rao: Minimum variance quadratic unbiased estimation of variance components. J. Multivariate Anal. (1971) I, 445-456. DOI 10.1016/0047-259X(71)90019-4 | MR 0301870 | Zbl 0259.62061
[4] C. R. Rao: Linear statistical inference and its applications. J. Wiley, New York 1973. MR 0346957 | Zbl 0256.62002
[5] C. R. Rao S. K. Mitra: Generalized inverse of matrices and its applications. J. Wiley, New York 1972. MR 0338013
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