In this article a sentence in Appendix 1, regarding least absolute deviations (LAD or L1 norm) method, is misleading. The author says (page 224, second column)
‘… two major difficulties have impeded its general adoption. Firstly, there are no closed-form formulae for evaluating b0 or b1 . . .’
In fact, the optimal values b0 and b1 are the solutions of the following linear programming problem:
subject to
i = 1 …, N, N number of observations, that can be solved using the Simplex method. A detailed analysis may be seen, for instance, in the excellent book ‘Linear programming’ by V. Chvátal.21
I think that Dr. Hedges is well aware of the solution because it is explained in some of the references of his paper, but a non-experienced reader may have the feeling that only approximate solutions exist.
Author's reply
Those readers familiar with Hudson's equation will have noticed a printing error in equation (5) of the paper. It should have read7
Those readers unfamiliar with Hudson's equation should now be able to make greater sense of the associated text.
Dr Jacovkis is thanked for emphasising the fact that, while use of the least-absolute-deviations (LAD) regression method may be a little more difficult than fitting using the least-squares (LS) procedure, there is no implication that the method is any more approximate. Chvátal's book21 could usefully have been added to the list of references in the paper.
