Least absolute value and chebychev estimation utilizing least squares results

In exploratory data analysis and curve fitting in particular, it is often desirable to observe residual values obtained with different estimation criteria. The goal with most linear model curve-fitting procedures is to minimize, in some sense, the vector of residuals. Perhaps three of the most common estimation criteria require minimizing: the sum of the absolute residuals (least absolute value or L1 norm); the sum of the squared residuals (least squares or L2 norm); and the maximum residual (Chebychev or L∞ norm). This paper demonstrates that utilizing the least squares residuals to provide an advanced start for the least absolute value and Chebychev procedures results in a significant reduction in computational effort. Computational results are provided.