Canadian Journal of Statistics

Consistent directions for least‐squares estimates

Journal Article


The least‐squares estimate θn = Xn+yn of the parameter θ in the linear model Yn = Xnθ + ϵn may not be consistent, but there may be directions u such that un tends to u'θ in some sense. This set of directions u has been characterized in two different papers: Drygas (1976) and Wu (1980). The conditions for consistency appear to be different in the two papers. The purpose of this note is to show that the two conditions are equivalent and that they both show that the consistent directions depend upon the geometry of the row vectors vi, i = 1,…, n, of Xn with respect to the direction u.

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