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On the relative goodness of ordinary least squares estimation in the general linear model. (English) Zbl 0652.62050
Acta Universitatis Tamperensis. Ser. A, Vol. 216. Tampere: University of Tampere. VI, 132 p. (1987).
This thesis consists of four papers and a summary and deals with the estimation of the mean vector in the general linear model. The relative goodness of ordinary least squares (OLS) estimation with respect to the best linear unbiased estimator (BLUE) is a concept which plays an important role in this research. The main contributions, however, are not directly concerned with the relative performance of OLS. The most fruitful concept in this research appears to concern the canonical correlations between the ordinary least squares fitted values and the residuals. The relative goodness of the ordinary least squares estimator of the parameter vector in the general linear model can be expressed as a function of these canonical correlations. In this thesis various properties of these canonical correlations are examined when the covariance matrix of the error vector is allowed to be singular and the model matrix may not have a full column rank.

MSC:
62H20 Measures of association (correlation, canonical correlation, etc.)
62J05 Linear regression; mixed models
62J99 Linear inference, regression