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Reduction of the dimension in the linear model with stochastic regressors. (English) Zbl 0555.62057
First of all we introduce the linear model with stochastic regressors. The estimates of the parmater \({\mathbb{B}}\) and \(\sigma^ 2_{Y/X}\) of this model are influenced by multicollinearity. As one of the possibilities to reduce the degree of multicollinearity subset regression is proposed. As a criterion for the selection of a model for the best extrapolation we use the mean square error of extrapolation. Some important properties of the estimates of the selected model will be shown.
MSC:
62J05 Linear regression; mixed models
62J99 Linear inference, regression
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