Adaptive Robust Regression by Using a Nonlinear Regression Program

Robust regression procedures have considerable attention in mathematical statistics literature. They, however, have not received nearly as much attention by practitioners performing data analysis. A contributing factor to this may be the lack of availability of these procedures in commonly used statistical software. In this paper we propose algorithms for obtaining parameter estimates and their asymptotic standard errors when fitting regression models to data assuming normal/independent errors. The algorithms proposed can be implemented in the commonly available nonlinear regression programs. We review a nubmer of previously proposed algorithms. As we discuss, these require special code and are difficult to implement in a nonlinear regression program. Methods of implementing the proposed algorithms in SAS-NLIN is discussed. Specifically, the two applications of regeression with the t and the slash family errors are discussed in detail. SAS NLIN and S-plus instructions are given for these two examples. Minor modification of these instructions can solve other problems at hand.