A model where the least trimmed squares estimator is maximum likelihood

Abstract

Abstract The least trimmed squares (LTS) estimator is a popular robust regression estimator. It finds a subsample of h ‘good’ observations among n observations and applies least squares on that subsample. We formulate a model in which this estimator is maximum likelihood. The model has ‘outliers’ of a new type, where the outlying observations are drawn from a distribution with values outside the realized range of h ‘good’, normal observations. The LTS estimator is found to be h1/2 consistent and asymptotically standard normal in the location-scale case. Consistent estimation of h is discussed. The model differs from the commonly used ϵ-contamination models and opens the door for statistical discussion on contamination schemes, new methodological developments on tests for contamination as well as inferences based on the estimated good data.