Constructing Regressions with Controlled Features: A Method of Probing Regression Performance

Studies of robust regression algorithms have generally relied on Monte Carlo trials and have concentrated on evaluating the algorithm's performance for long-tailed error distributions. This article identifies other aspects of data structure that can influence the performance of robust regression procedures and presents an algorithm for constructing regression problems in which each of these factors can be controlled separately. The method generalizes to multiple regression the sensitivity function introduced by Tukey. We illustrate the method on M-estimate regressions computed by the publicly available package, ROSEPACK. This experiment confirms the importance of controlling the structure of the predictors and helps to account for anomalous results reported in several published studies.