Asymptotic properties of the growth curve model with covariance components

Ivan Žežula

Applications of Mathematics (1997)

  • Volume: 42, Issue: 1, page 57-69
  • ISSN: 0862-7940

Abstract

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We consider a multivariate regression (growth curve) model of the form Y = X B Z + ε , E ε = 0 , var ( vec ε ) = W ⊗ Σ , where W = ∑ i = 1 k θ i V i and θ i ’s are unknown scalar covariance components. In the case of replicated observations, we derive the explicit form of the locally best estimators of the covariance components under normality and asymptotic confidence ellipsoids for certain linear functions of the first order parameters { B i j } estimating simultaneously the first and the second order parameters.

How to cite

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Žežula, Ivan. "Asymptotic properties of the growth curve model with covariance components." Applications of Mathematics 42.1 (1997): 57-69. <http://eudml.org/doc/32967>.

@article{Žežula1997,
abstract = {We consider a multivariate regression (growth curve) model of the form $Y = XBZ + \varepsilon $, $\operatorname\{E\}\varepsilon =0$, $\operatorname\{var\}(\operatorname\{vec\}\varepsilon ) = W \otimes \Sigma $, where $W = \sum _\{i=1\}^\{k\} \theta _i V_i$ and $\theta _i$’s are unknown scalar covariance components. In the case of replicated observations, we derive the explicit form of the locally best estimators of the covariance components under normality and asymptotic confidence ellipsoids for certain linear functions of the first order parameters $\lbrace B_\{ij\}\rbrace $ estimating simultaneously the first and the second order parameters.},
author = {Žežula, Ivan},
journal = {Applications of Mathematics},
keywords = {replicated growth curve model; covariance components; multivariate regression; asymptotic confidence region; replicated growth curve model; covariance components; multivariate regression; asymptotic confidence regions},
language = {eng},
number = {1},
pages = {57-69},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Asymptotic properties of the growth curve model with covariance components},
url = {http://eudml.org/doc/32967},
volume = {42},
year = {1997},
}

TY - JOUR
AU - Žežula, Ivan
TI - Asymptotic properties of the growth curve model with covariance components
JO - Applications of Mathematics
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 42
IS - 1
SP - 57
EP - 69
AB - We consider a multivariate regression (growth curve) model of the form $Y = XBZ + \varepsilon $, $\operatorname{E}\varepsilon =0$, $\operatorname{var}(\operatorname{vec}\varepsilon ) = W \otimes \Sigma $, where $W = \sum _{i=1}^{k} \theta _i V_i$ and $\theta _i$’s are unknown scalar covariance components. In the case of replicated observations, we derive the explicit form of the locally best estimators of the covariance components under normality and asymptotic confidence ellipsoids for certain linear functions of the first order parameters $\lbrace B_{ij}\rbrace $ estimating simultaneously the first and the second order parameters.
LA - eng
KW - replicated growth curve model; covariance components; multivariate regression; asymptotic confidence region; replicated growth curve model; covariance components; multivariate regression; asymptotic confidence regions
UR - http://eudml.org/doc/32967
ER -

References

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