Benchmark testing of algorithms for very robust regression: FS, LMS and LTS

The methods of very robust regression resist up to 50% of outliers. The algorithms for very robust regression rely on selecting numerous subsamples of the data. New algorithms for LMS and LTS estimators that have increased computational efficiency due to improved combinatorial sampling are proposed. These and other publicly available algorithms are compared for outlier detection. Timings and estimator quality are also considered. An algorithm using the forward search (FS) has the best properties for both size and power of the outlier tests.