Applications and algorithms for least trimmed sum of absolute deviations regression

High breakdown estimation (HBE) addresses the problem of getting reliable parameter estimates in the face of outliers that may be numerous and badly placed. In multiple regression, the standard HBE’s have been those defined by the least median of squares (LMS) and the least trimmed squares (LTS) criteria. Both criteria lead to a partitioning of the data set’s n cases into two “halves ” – the covered “half ” of cases are accommodated by the fit, while the uncovered “half”, which is intended to include any outliers, are ignored. In LMS, the criterion is the Chebyshev norm of the residuals of the covered cases, while in LTS the criterion is the sum of squared residuals of the covered cases. Neither LMS nor LTS is ∗Douglas M. Hawkins is Professor and David Olive is Visiting Assistant Professor, School of Statistics, University of Minnesota, St. Paul, MN 55108, U S A. The authors are grateful to the editors and referees for a number of helpful suggestions for improvement in the article. 1 entirely satisfactory. LMS has a statistical efficiency of zero if the true residual