ON THE DESIGN OF ROBUST REGRESSION-ESTIMATORS

The major advantage of applying classical least-squares to multi-param eter regression is that the most efficient unbiased estimates of the p arameters can be obtained when observations are coming from a normal p opulation. These estimates, however, may loose their reliability and e fficiency when the normal distribution is contaminated by gross errors . Against the deficiency of the traditional least-squares, robust esti mators based on two ''contaminated'' normal distribution models are pr oposed in this paper. Then the efficiency and reliability of these rob ust estimators is evaluated when the distribution in the contaminated part is unknown. Comparisons between the robust and classical estimato rs for different types of data are also made. Finally, a numerical exa mple is presented to illustrate how to apply the robust estimators to real data.