MEDIAN ESTIMATES IN SIMPLE LINEAR REGRESSION

Summary
Estimates in simple linear regression which minimize the sum of absolute values of residuals are discussed. These estimates, called median-estimates , are an analogue of the sample median, and their properties reflect this. A simple graphical procedure, related to an early (1923) one of Edgeworth, is outlined for computing median estimates. This method works well in small or moderate samples, and is demonstrated on two examples. The small sample distribution of the median estimates is examined by conditioning on the pattern of signs of the residuals, and the resulting conditional distribution gives qualitative information on the adequacy of the approximation of the exact distribution by the (known) asymptotic distibution.