Estimation of variance components in mixed linear models

Júlia Volaufová; Viktor Witkovský

Applications of Mathematics (1992)

  • Volume: 37, Issue: 2, page 139-148
  • ISSN: 0862-7940

Abstract

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The MINQUE of the linear function ' ϑ of the unknown variance-components parameter ϑ in mixed linear model under linear restrictions of the type 𝐑 ϑ = c is defined and derived. As an illustration of this estimator the example of the one-way classification model with the restrictions ϑ 1 = k ϑ 2 , where k 0 , is given.

How to cite

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Volaufová, Júlia, and Witkovský, Viktor. "Estimation of variance components in mixed linear models." Applications of Mathematics 37.2 (1992): 139-148. <http://eudml.org/doc/15705>.

@article{Volaufová1992,
abstract = {The MINQUE of the linear function $\int ^\{\prime \}\vartheta $ of the unknown variance-components parameter $\vartheta $ in mixed linear model under linear restrictions of the type $\mathbf \{R\}\vartheta = c$ is defined and derived. As an illustration of this estimator the example of the one-way classification model with the restrictions $\vartheta _1 = k\vartheta _2$, where $k \ge 0$, is given.},
author = {Volaufová, Júlia, Witkovský, Viktor},
journal = {Applications of Mathematics},
keywords = {minimum invariant quadratic estimators; MINQUE; mixed linear model; linear restrictions; one-way classification model; minimum invariant quadratic estimators; MINQUE; mixed linear model; linear restrictions; one-way classification model},
language = {eng},
number = {2},
pages = {139-148},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Estimation of variance components in mixed linear models},
url = {http://eudml.org/doc/15705},
volume = {37},
year = {1992},
}

TY - JOUR
AU - Volaufová, Júlia
AU - Witkovský, Viktor
TI - Estimation of variance components in mixed linear models
JO - Applications of Mathematics
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 2
SP - 139
EP - 148
AB - The MINQUE of the linear function $\int ^{\prime }\vartheta $ of the unknown variance-components parameter $\vartheta $ in mixed linear model under linear restrictions of the type $\mathbf {R}\vartheta = c$ is defined and derived. As an illustration of this estimator the example of the one-way classification model with the restrictions $\vartheta _1 = k\vartheta _2$, where $k \ge 0$, is given.
LA - eng
KW - minimum invariant quadratic estimators; MINQUE; mixed linear model; linear restrictions; one-way classification model; minimum invariant quadratic estimators; MINQUE; mixed linear model; linear restrictions; one-way classification model
UR - http://eudml.org/doc/15705
ER -

References

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  1. C. R. Rao, Estimation of variance and covariance components - MINQUE theory, Journal of Multivariate Analysis 1 (1971), 267-275. (1971) Zbl0223.62086MR0301869
  2. C. R. Rao, J. Kleffe, Estimation of Variance Components and Applications, volume 3 of Statistics and probability, North-Holland, Amsterdam, New York, Oxford, Tokyo, 1988, first edition. (1988) Zbl0645.62073MR0933559
  3. C. R. Rao, S. K. Mitra, Generalized Inverse of Matrices and Its Applications, John Wiley & Sons, New York, London, Sydney, Toronto, 1971, first edition. (1971) Zbl0236.15005MR0338013
  4. J. Seely, Linear spaces and unbiased estimation, Ann. Math. Stat. 41 (1970), 1725-1734. (1970) Zbl0263.62041MR0275559
  5. L. R. Verdooren, Practical aspects of variance component estimation, invited lecture for the 4th International Summer School on Problems of Model Choice and Parameter Estimation in Regression Analysis Mülhausen, GDR, May 1979. (1979) 
  6. G. Zyskind, On canonical forms, negative covariance matrices and best and simple least square estimator in linear models, Ann. Math. Stat. 38 (1967), 1092-1110. (1967) MR0214237

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