Displaying similar documents to “Some properties of the best linear unbiased estimators in multivariate growth curve models.”

On the equality of the ordinary least squares estimators and the best linear unbiased estimators in multivariate growth-curve models.

Gabriela Beganu (2007)

RACSAM

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It is well known that there were proved several necessary and sufficient conditions for the ordinary least squares estimators (OLSE) to be the best linear unbiased estimators (BLUE) of the fixed effects in general linear models. The purpose of this article is to verify one of these conditions given by Zyskind [39, 40]: there exists a matrix Q such that ΩX = XQ, where X and Ω are the design matrix and the covariance matrix, respectively. It will be shown the accessibility of this condition...

Overview of Recent Results in Growth-curve-type Multivariate Linear Models

Ivan Žežula, Daniel Klein (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The Extended Growth Curve Model (ECGM) is a multivariate linear model connecting different multivariate regression models in sample subgroups through common variance matrix. It has the form: Y = i = 1 k X i B i Z i ' + e , vec ( e ) N n × p 0 , Σ I n . Here, matrices X i contain subgroup division indicators, and Z i corresponding regressors. If k = 1 , we speak about (ordinary) Growth Curve Model. The model has already its age (it dates back to 1964), but it has many important applications. That is why it is still intensively studied. Many articles investigating...

On some alternative forms equivalent to Kruskal's condition for OLSE to be BLUE.

Gabriela Beganu (2007)

RACSAM

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The necessary and sufficient condition for the ordinary least squares estimators (OLSE) to be the best linear unbiased estimators (BLUE) of the expected mean in the general univariate linear regression model was given by Kruskal (1968) using a coordinate-free approach. The purpose of this article is to present in the same manner some alternative forms of this condition and to prove two of the Haberman’s equivalent conditions in a different and simpler way. The results obtained in the...

Estimation of the first order parameters in the twoepoch linear model

Karel Hron (2007)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The linear regression model, where the mean value parameters are divided into stable and nonstable part in each of both epochs of measurement, is considered in this paper. Then, equivalent formulas of the best linear unbiased estimators of this parameters in both epochs using partitioned matrix inverse are derived.

Seemingly unrelated regression models

Lubomír Kubáček (2013)

Applications of Mathematics

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The cross-covariance matrix of observation vectors in two linear statistical models need not be zero matrix. In such a case the problem is to find explicit expressions for the best linear unbiased estimators of both model parameters and estimators of variance components in the simplest structure of the covariance matrix. Univariate and multivariate forms of linear models are dealt with.