Graduate Thesis Or Dissertation
 

Empirical studies on the estimation of variances in linear regression models

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  • An iterative approach is suggested for the estimation of the error covariance matrix [sigma] to find approximate BLUE estimators in linear regression models. It is shown through experimental studies how the variances can be estimated in the simple general linear regression model, in the linear regression model sequenced over time, and in the linear regression model with a stochastically varying parameter vector, commonly called the Kalman model. All studies assume the true error covariance matrix [sigma] to be diagonal. The general linear regression model is shown to be a special case of the Kalman model. Bounds are found for the covariance matrix of the parameter vector estimation error of the Kalman model. They show the parameter vector estimator in the Kalman model to be an inconsistent estimator of the true parameter vector with consistency applying only when the true parameter vector is nonrandom.
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