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Bayes unbiased estimation in a model with two variance components
Applications of Mathematics, Tome 32 (1987) no. 2, pp. 120-130
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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.
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.
DOI : 10.21136/AM.1987.104241
Classification : 62C15, 62F15, 62J10, 62J99
Keywords: risk function; explicit expression; Bayes invariant quadratic unbiased estimate; linear function of the variance components; mixed linar model; normal case 
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Stuchlý, Jaroslav. Bayes unbiased estimation in a model with two variance components. Applications of Mathematics, Tome 32 (1987) no. 2, pp. 120-130. doi: 10.21136/AM.1987.104241

[1] S. Gnot J. Kleffe: Quadratic estimation in mixed linear models with two variance components. Journal of statistical planning and Inference 8 (1983) 267-279. | DOI | MR

[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 | MR | Zbl

[4] C. R. Rao: Linear statistical inference and its applications. J. Wiley, New York 1973. | MR | Zbl

[5] C. R. Rao S. K. Mitra: Generalized inverse of matrices and its applications. J. Wiley, New York 1972. | MR

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