Properties of $L\sp 1$ residuals
Stephan Morgenthaler · Lecture notes-monograph series · 1997
The paper discusses the behavior of residuals from least-absolutedeviations (or L 1 ) fits of linear models.Particular emphasis is given to data arising by way of designed experiments.The paper argues that the L 1 method of fitting such models should be discouraged.The method is inefficient when compared to other robust methods while not being any simpler to compute.The residuals obtained by L 1 fitting exhibit several weaknesses.First of all they are ambiguous in the sense that there are a multitude of L 1 fits, sometimes quite far apart.Second, typical algorithms produce as many exact zero residuals as there are contrasts fitted.As a result, the non zero residuals do not give an accurate reflection of the errors that occurred during the experimental runs.