A robust multivariate regression algorithm with robust estimators

The robust regression problem is considered. A (1-∈)-fraction of the given data, 0 < ∈ < 1/2, obeys a multivariate linear model with unknown parameters. The remaining ∈-fraction obeys a completely different model or models. The authors develop a procedure for estimating the parameters of the linear model from the contaminated data. They use a divide-and-conquer approach. They solve the problem using only one-dimensional robust estimators like that of P. J. Huber (1981). They illustrate their method with two examples which pose considerable difficulty to all methods except the LMS (least mean squares) method. The computational load of the present method is a small fraction of that of the LMS method