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Generalized Least-Squares Regressions I: Efficient Derivations, Nataniel Greene
Generalized Least-Squares Regressions I: Efficient Derivations, Nataniel Greene
Publications and Research
Ordinary least-squares regression suffers from a fundamental lack of symmetry: the regression line of y given x and the regression line of x given y are not inverses of each other. Alternative symmetric regression methods have been developed to address this concern, notably: orthogonal regression and geometric mean regression. This paper presents in detail a variety of least squares regression methods which may not have been known or fully explicated. The derivation of each method is made efficient through the use of Ehrenberg's formula for the ordinary least-squares error and through the extraction of a weight function g(b) which characterizes …
Generalized Least-Squares Regressions Ii: Theory And Classification, Nataniel Greene
Generalized Least-Squares Regressions Ii: Theory And Classification, Nataniel Greene
Publications and Research
In the first paper of this series, a variety of known and new symmetric and weighted least-squares regression methods were presented with efficient derivations. This paper continues and generalizes the previous work with a theory for deriving, analyzing, and classifying all symmetric and weighted least-squares regression methods.