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Bayes unbiased estimation in a model with three variance components
Applications of Mathematics, Tome 34 (1989) no. 5, pp. 375-386
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In the paper necessary and sufficient conditions for the existence and an explicit expression for the Bayes invariant quadratic unbiased estimate of the linear function of the variance components are presented for the mixed linear model $\bold{t=X\beta + \epsilon}$, $\bold{E(t)=X\beta}$, $\bold {Var(t)=0_1U_1 + 0_2U_2 + 0_3U_3}$, with three unknown variance components in the normal case. An application to some examples from the analysis of variance is given.
In the paper necessary and sufficient conditions for the existence and an explicit expression for the Bayes invariant quadratic unbiased estimate of the linear function of the variance components are presented for the mixed linear model $\bold{t=X\beta + \epsilon}$, $\bold{E(t)=X\beta}$, $\bold {Var(t)=0_1U_1 + 0_2U_2 + 0_3U_3}$, with three unknown variance components in the normal case. An application to some examples from the analysis of variance is given.
DOI : 10.21136/AM.1989.104365
Classification : 62F15, 62H12, 62J10, 62J99
Keywords: necessary and sufficient conditions for an existence; Bayes invariant quadratic unbiased estimate; linear function of variance components; mixed linear model; three unknown variance components; normal case 
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Stuchlý, Jaroslav. Bayes unbiased estimation in a model with three variance components. Applications of Mathematics, Tome 34 (1989) no. 5, pp. 375-386. doi: 10.21136/AM.1989.104365

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

[2] J. Kleffe R. Pincus: Bayes and best quadratic unbiased estimators for parameters of the covariance matrix in a normal linear model. Math. Operationsf. Statist. 5 (1974), 43 - 67. | DOI | MR

[3] A. Olsen J. Seely D. Birkes: Invariant quadratic unbiased estimation for two variance components. Ann. Statist. 4 (1976), 878-890. | DOI | MR

[4] C. R. Rao: Linear Statistical Inference and Its Applications. 2nd ed. J. Wiley, New York 1973. | MR | Zbl

[5] C. R. Rao: Minimum variance quadratic unbiased estimation of variance components. J. Multivariate Anal. I (1971), 445-456. | DOI | MR | Zbl

[6] J. Stuchlý: Bayes unbiased estimation in a model with two variance components. Aplikace matematiky 32, No. 2 (1987), 120-130. | MR

[7] S. Zacks: The Theory of Statistical Inference. J. Wiley, New York, 1971. | MR

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