Review

Abstract

Although this study has not yet been completed, the author believes, that a review of the preceding results is appropriate at this point. So far, the treatise on the statistical problem of searching for linear relations in observations has been purely theoretical. In chapters III, IV and V parameter matrices have been obtained as the optimal values of distance minimizing problems. They are observed as (explicitly or implicitly defined) functions of the population covariance matrix ∑. In chapter II an explanation has been given of how asymptotically normally distributed estimators of this class of parameters can be obtained, together with their large sample properties, given that the parameters in question are differentiable in ∑. It appeared that in order to apply the delta-method, the derivatives of the parameter matrices with respect to the elements of ∑ are needed. Therefore each section that discusses a distance minimizing parameter matrix B (or A), also provides the corresponding gradient matrix ∇(B;∑) (or ∇(A;∑)) of the partial derivatives. In chapter VII the Population-Sample Decomposition approach will be used to show how these distance minimizing parameters can be applied in practice, and it will be made clear which problems have to be overcome, in order to progam the PSD estimation technique efficiently.