Robustness of the best linear unbiased estimator and predictor in linear regression models

František Štulajter

Displaying similar documents to “Robustness of the best linear unbiased estimator and predictor in linear regression models”

Uncertainty of the design and covariance matrices in linear statistical model

Lubomír Kubáček, Jaroslav Marek (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

The aim of the paper is to determine an influence of uncertainties in design and covariance matrices on estimators in linear regression model.

Variance components and an additional experiment

Lubomír Kubáček (2012)

Applications of Mathematics

Similarity:

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.

Seemingly unrelated regression models

Lubomír Kubáček (2013)

Applications of Mathematics

Similarity:

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.

Asymptotic properties of the growth curve model with covariance components

Ivan Žežula (1997)

Applications of Mathematics

Similarity:

We consider a multivariate regression (growth curve) model of the form $Y = X B Z + ε$ , $E ε = 0$ , $var (vec ε) = W \otimes Σ$ , where $W = \sum_{i = 1}^{k} θ_{i} V_{i}$ 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.