This paper is a continuation of a previous paper [2] on the consistency of the least squares estimator ^ -+ aN-X Iv YN of 6 in the sequence of regression-models yu= X N (~ + u N obtained after N observations have been made. It is the purpose of this paper to show that the consistency-condition 2,~i,(X'NXN)--*oO can be obtained without any nornaality assumptions. This result was conjectured by Eicker (Ann. Math. Statist., 34, 447-456, (1963)). Moreover, it is shown, that under rather weak assumptions the sequence {X~ YN} possesses the remarkable property that lira X~v yN=Z in the sense of L2-convergence, whatever the sequence {XN} N~o~ may be.If the components of u N are supposed to be stochastically independent and there is only one regressor necessary and sufficient conditions for strong consistency of a N can be obtained. This result is then applied to obtain sufficient conditions for the strong consistency of a N in the general case. Moreover, it is shown that these conditions are met if N-iX~v XN--> Z, Z > 0, the usual assumption made in econometric textbooks to establish weak consistency. * This work was done when the author was a research worker at "Sonderforschungsbereich Okonometrie und Unternehmensforschung der Universit~it Bonn".
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