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Title: Bayes unbiased estimation in a model with two variance components (English)
Author: Stuchlý, Jaroslav
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 32
Issue: 2
Year: 1987
Pages: 120-130
Summary lang: English
Summary lang: Russian
Summary lang: Czech
Category: math
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. (English)
Keyword: risk function
Keyword: explicit expression
Keyword: Bayes invariant quadratic unbiased estimate
Keyword: linear function of the variance components
Keyword: mixed linar model
Keyword: normal case
MSC: 62C15
MSC: 62F15
MSC: 62J10
MSC: 62J99
idZBL: Zbl 0625.62019
idMR: MR0885759
DOI: 10.21136/AM.1987.104241
Date available: 2008-05-20T18:31:51Z
Last updated: 2020-07-28
Stable URL:
Reference: [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. MR 0729245, 10.1016/0378-3758(83)90045-9
Reference: [2] L. Kubáček: Fundaments of the theory of estimates.(Slovak). Veda, Publishing House of Slovak Acad. Sc., Bratislava 1983,.
Reference: [3] C. R. Rao: Minimum variance quadratic unbiased estimation of variance components.J. Multivariate Anal. (1971) I, 445-456. Zbl 0259.62061, MR 0301870, 10.1016/0047-259X(71)90019-4
Reference: [4] C. R. Rao: Linear statistical inference and its applications.J. Wiley, New York 1973. Zbl 0256.62002, MR 0346957
Reference: [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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