THE WEIGHTED MEDIAN AND MULTIPLE REGRESSION1

This paper reviews the iterative use of the weighted median to estimate the parameter vector in the classical linear model when the fitting criterion is (i) least absolute deviation sum (LAD); and (ii) the Cauchy criterion. The implications of the Cauchy criterion, little developed hitherto, are compared and contrasted with results for the better-known LAD procedure. Since the weighted median is essentially an estimation technique for the simplest regression model, its use in these contexts illustrates the central role in statistical theory that is played by regression analysis, a focal area of the work of E. J. Williams (1959).