Bayes unbiased estimation in a model with three variance components

Jaroslav Stuchlý

Aplikace matematiky (1989)

  • Volume: 34, Issue: 5, page 375-386
  • ISSN: 0862-7940

Abstract

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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 𝐭 = 𝐗 β + ϵ , 𝐄 ( 𝐭 ) = 𝐗 β , 𝐕𝐚𝐫 ( 𝐭 ) = 0 1 𝐔 1 + 0 2 𝐔 2 + 0 3 𝐔 3 , with three unknown variance components in the normal case. An application to some examples from the analysis of variance is given.

How to cite

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Stuchlý, Jaroslav. "Bayes unbiased estimation in a model with three variance components." Aplikace matematiky 34.5 (1989): 375-386. <http://eudml.org/doc/15591>.

@article{Stuchlý1989,
abstract = {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 $\mathbf \{t=X\beta + \epsilon \}$, $\mathbf \{E(t)=X\beta \}$, $\mathbf \{Var(t)=0_1U_1 + 0_2U_2 + 0_3U_3\}$, with three unknown variance components in the normal case. An application to some examples from the analysis of variance is given.},
author = {Stuchlý, Jaroslav},
journal = {Aplikace matematiky},
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; 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},
language = {eng},
number = {5},
pages = {375-386},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bayes unbiased estimation in a model with three variance components},
url = {http://eudml.org/doc/15591},
volume = {34},
year = {1989},
}

TY - JOUR
AU - Stuchlý, Jaroslav
TI - Bayes unbiased estimation in a model with three variance components
JO - Aplikace matematiky
PY - 1989
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 34
IS - 5
SP - 375
EP - 386
AB - 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 $\mathbf {t=X\beta + \epsilon }$, $\mathbf {E(t)=X\beta }$, $\mathbf {Var(t)=0_1U_1 + 0_2U_2 + 0_3U_3}$, with three unknown variance components in the normal case. An application to some examples from the analysis of variance is given.
LA - eng
KW - 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; 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
UR - http://eudml.org/doc/15591
ER -

References

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  1. S. Gnot J. Kleffe, 10.1016/0378-3758(83)90045-9, Journal of Statist. Planning and Inference 8 (1983), 267-279. (1983) Zbl0561.62064MR0729245DOI10.1016/0378-3758(83)90045-9
  2. J. Kleffe R. Pincus, 10.1080/02331887408801147, Math. Operationsf. Statist. 5 (1974), 43 - 67. (1974) Zbl0277.62027MR0341683DOI10.1080/02331887408801147
  3. A. Olsen J. Seely D. Birkes, 10.1214/aos/1176343586, Ann. Statist. 4 (1976), 878-890. (1976) Zbl0344.62060MR0418345DOI10.1214/aos/1176343586
  4. C. R. Rao, Linear Statistical Inference and Its Applications, 2nd ed. J. Wiley, New York 1973. (1973) Zbl0256.62002MR0346957
  5. C. R. Rao, 10.1016/0047-259X(71)90019-4, J. Multivariate Anal. I (1971), 445-456. (1971) Zbl0259.62061MR0301870DOI10.1016/0047-259X(71)90019-4
  6. J. Stuchlý, Bayes unbiased estimation in a model with two variance components, Aplikace matematiky 32, No. 2 (1987), 120-130. (1987) Zbl0625.62019MR0885759
  7. S. Zacks, The Theory of Statistical Inference, J. Wiley, New York, 1971. (1971) MR0420923

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