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variance components; plug-in estimator; multivariate models
Variance components in regression models are usually unknown. They must be estimated and it leads to a construction of plug–in estimators of the parameters of the mean value of the observation matrix. Uncertainty of the estimators of the variance components enlarge the variances of the plug–in estimators. The aim of the paper is to find this enlargement.
[1] Fišerová, E., Kubáček, L., Kunderová, P.: Linear Statistical Models: Regularity and Singularities. Academia, Praha, 2007.
[2] Kubáček, L.: Multivariate Statistical Models Revisited. Vyd. University Palackého, Olomouc, 2008.
[3] Rao, C. R., Mitra, S. K.: Generalized Inverse of Matrices and its Applications. Wiley, New York–London–Sydney–Toronto, 1971. MR 0338013 | Zbl 0236.15005
[4] Rao, C. R., Kleffe, J.: Estimation of Variance Components and Applications. North–Holland, Amsterdam–New York–Oxford–Tokyo, 1988. MR 0933559 | Zbl 0645.62073
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