PROC ROBUSTREG implements algorithms to detect outliers and provide resistant (stable) results in the presence of outliers. The ROBUSTREG procedure provides four such methods: M estimation, LTS estimation, S estimation, and MM estimation.
M estimation, which was introduced by Huber (1973), is the simplest approach both computationally and theoretically. Although it is not robust with respect to leverage points, it is still used extensively in analyzing data for which it can be assumed that the contamination is mainly in the response direction.
Least trimmed squares (LTS) estimation is a high breakdown value method that was introduced by Rousseeuw (1984). The breakdown value is a measure of the proportion of observations that are contaminated by outliers that an estimation method can withstand and still maintain its robustness.
S estimation is a high breakdown value method that was introduced by Rousseeuw and Yohai (1984). When the breakdown value is the same, it has a higher statistical efficiency than LTS estimation.
MM estimation, which was introduced by Yohai (1987), combines high breakdown value estimation and M estimation. It has the high breakdown property of S estimation but a higher statistical efficiency.
For diagnostic purposes, PROC ROBUSTREG also implements robust leverage-point detection based on the robust Mahalanobis distance. The robust distance is computed by using a generalized minimum covariance determinant (MCD) algorithm.