# Bayes unbiased estimation in a model with two variance components

Aplikace matematiky (1987)

• Volume: 32, Issue: 2, page 120-130
• ISSN: 0862-7940

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## Abstract

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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 $𝐭=𝐗\beta +ϵ$, $𝐄\left(𝐭\right)=𝐗\beta$, $𝐃\left(𝐭\right)={\mathbf{0}}_{\mathbf{1}}{𝐔}_{\mathbf{1}}+{\mathbf{0}}_{\mathbf{2}}{𝐔}_{\mathbf{2}}$ with the unknown variance componets in the normal case. The matrices ${𝐔}_{\mathbf{1}}$, ${𝐔}_{\mathbf{2}}$ may be singular. Applications to two examples of the analysis of variance are given.

## How to cite

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Stuchlý, Jaroslav. "Bayes unbiased estimation in a model with two variance components." Aplikace matematiky 32.2 (1987): 120-130. <http://eudml.org/doc/15484>.

@article{Stuchlý1987,
abstract = {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 $\mathbf \{t=X\beta +\epsilon \}$, $\mathbf \{E(t)=X\beta \}$, $\mathbf \{D(t)=0_1U_1+0_2U_2\}$ with the unknown variance componets in the normal case. The matrices $\mathbf \{U_1\}$, $\mathbf \{U_2\}$ may be singular. Applications to two examples of the analysis of variance are given.},
author = {Stuchlý, Jaroslav},
journal = {Aplikace matematiky},
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},
language = {eng},
number = {2},
pages = {120-130},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bayes unbiased estimation in a model with two variance components},
url = {http://eudml.org/doc/15484},
volume = {32},
year = {1987},
}

TY - JOUR
AU - Stuchlý, Jaroslav
TI - Bayes unbiased estimation in a model with two variance components
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 2
SP - 120
EP - 130
AB - 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 $\mathbf {t=X\beta +\epsilon }$, $\mathbf {E(t)=X\beta }$, $\mathbf {D(t)=0_1U_1+0_2U_2}$ with the unknown variance componets in the normal case. The matrices $\mathbf {U_1}$, $\mathbf {U_2}$ may be singular. Applications to two examples of the analysis of variance are given.
LA - eng
KW - 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
UR - http://eudml.org/doc/15484
ER -

## References

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1. S. Gnot J. Kleffe, 10.1016/0378-3758(83)90045-9, Journal of statistical planning and Inference 8 (1983) 267-279. (1983) Zbl0561.62064MR0729245DOI10.1016/0378-3758(83)90045-9
2. L. Kubáček, Fundaments of the theory of estimates, (Slovak). Veda, Publishing House of Slovak Acad. Sc., Bratislava 1983,. (1983)
3. C. R. Rao, 10.1016/0047-259X(71)90019-4, J. Multivariate Anal. (1971) I, 445-456. (1971) Zbl0259.62061MR0301870DOI10.1016/0047-259X(71)90019-4
4. C. R. Rao, Linear statistical inference and its applications, J. Wiley, New York 1973. (1973) Zbl0256.62002MR0346957
5. C. R. Rao S. K. Mitra, Generalized inverse of matrices and its applications, J. Wiley, New York 1972. (1972) Zbl0261.62051MR0338013

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