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In this paper we show how a variant of Stone and Brook's continuum regression criterion may be used to define the least variance ratio estimator of the slope parameters of the simultaneous equations model of econometrics. As a by-product of this approach we identify a family of estimators (distinct from the family of k-class estimators) to which it and two variants of the orthogonal least squares estimator belong. We also take the opportunity to mention several features of linear unbiased scalar residuals omitted from an earlier paper. [ABSTRACT FROM AUTHOR]

The two-variable orthogonal least squares procedure was developed independently by Julius Ludwig Weisbach (1806–1871) and Robert Jackson Adcock (1826–1895). In this article we discuss aspects of two recent articles concerned with the contributions of these individuals. We also identify a prototype of the orthogonal minimax fitting procedure due to August Beyer (1677–1753). [ABSTRACT FROM AUTHOR]