On Edgeworth's method for minimum absolute error linear regression

The Edgeworth (1887) algorithm for minimizing absolute error is known to suffer from convergence problems when the data contains degeneracies. In this paper, it is shown that for the particular problem of fitting a line to a set of uniformly sampled data, the problem of degeneracy may be easily avoided by utilizing a stable sorter for the weighted median operation needed in Edgeworth's method. Proof of convergence is based on establishing an equivalence between the use of a stable sorting routine and perturbing the original data in such a way that no degeneracies exist. In addition, it will be shown that the data set size may be selected so that the minimum error fit is unique.<
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