Quadratic estimations in mixed linear models

Štefan Varga

Applications of Mathematics (1991)

  • Volume: 36, Issue: 2, page 134-144
  • ISSN: 0862-7940

Abstract

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In the paper four types of estimations of the linear function of the variance components are presented for the mixed linear model 𝐘 = 𝐗 β + 𝐞 with expectation E ( 𝐘 ) = 𝐗 β and covariance matrix D ( 𝐘 ) = 0 1 𝐕 1 + . . . + 0 𝐦 𝐕 𝐦 .

How to cite

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Varga, Štefan. "Quadratic estimations in mixed linear models." Applications of Mathematics 36.2 (1991): 134-144. <http://eudml.org/doc/15665>.

@article{Varga1991,
abstract = {In the paper four types of estimations of the linear function of the variance components are presented for the mixed linear model $\mathbf \{Y=X \beta + e\}$ with expectation $E(\mathbf \{Y)=X \beta \}$ and covariance matrix $D(\mathbf \{Y)=0_1V_1 + ... + 0_mV_m\}$.},
author = {Varga, Štefan},
journal = {Applications of Mathematics},
keywords = {mixed linear model; minimum norm quadratic estimation; variance components; first order fixed parameter unknowns; second order fixed parameter unknowns; invariant for translations; mixed linear models; minimum norm quadratic estimations; first order fixed parameter unknowns; second order fixed parameter unknowns; linear functions of variance components; invariant for translations},
language = {eng},
number = {2},
pages = {134-144},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Quadratic estimations in mixed linear models},
url = {http://eudml.org/doc/15665},
volume = {36},
year = {1991},
}

TY - JOUR
AU - Varga, Štefan
TI - Quadratic estimations in mixed linear models
JO - Applications of Mathematics
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 36
IS - 2
SP - 134
EP - 144
AB - In the paper four types of estimations of the linear function of the variance components are presented for the mixed linear model $\mathbf {Y=X \beta + e}$ with expectation $E(\mathbf {Y)=X \beta }$ and covariance matrix $D(\mathbf {Y)=0_1V_1 + ... + 0_mV_m}$.
LA - eng
KW - mixed linear model; minimum norm quadratic estimation; variance components; first order fixed parameter unknowns; second order fixed parameter unknowns; invariant for translations; mixed linear models; minimum norm quadratic estimations; first order fixed parameter unknowns; second order fixed parameter unknowns; linear functions of variance components; invariant for translations
UR - http://eudml.org/doc/15665
ER -

References

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  1. J. Kleffe, Best quadratic unbiased estimators for variance components in mixed linear models, Sankhya, 38 (1976), 179-186. (1976) Zbl0413.62052MR0468051
  2. C. R. Rao, Estimation of variance and covariance components - MINQUE theory, Journ. Multivariant. Analysis, 1 (1971), 257-275. (1971) Zbl0223.62086MR0301869
  3. C. R. Rao K. S. Mitra, Generalized Inverse of Matrices and its Application, J. Wiley, N. York 1971. (1971) MR0338013
  4. C. R. Rao J. Kleffe, Estimation of Variance Components, In: P. R. Krisnaiah, ed. Handbook of Statistics, Vol. I. North Holland, N. York, (1980), 1-40. (1980) 
  5. Š. Varga, Minimum Variance Quadratic Unbiased Estimation of Variance Components, Math. Slovaca, 36 No. 2 (1986), 163-170. (1986) Zbl0605.62077MR0849707
  6. Š. Varga, Estimations in Mixed Linear Models, Sborník VŠCHT Praha Řada M - Matematika, (1990), 1-10. (1990) 

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