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Lubomír Kubáček (2012)
Applications of Mathematics
Estimators of parameters of an investigated object can be considered after some time as insufficiently precise. Therefore, an additional measurement must be realized. A model of a measurement, taking into account both the original results and the new ones, has a litle more complicated covariance matrix, since the variance components occur in it. How to deal with them is the aim of the paper.
Lubomír Kubáček, Eva Tesaříková (2006)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
Unknown parameters of the covariance matrix (variance components) of the observation vector in regression models are an unpleasant obstacle in a construction of the best estimator of the unknown parameters of the mean value of the observation vector. Estimators of variance componets must be utilized and then it is difficult to obtain the distribution of the estimators of the mean value parameters. The situation is more complicated in the case of nonlinearity of the regression model. The aim of the...
Lubomír Kubáček, Jana Vrbková (2013)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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.
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