A model where the least trimmed squares estimator is maximum likelihood
Vanessa Berenguer-Rico, Søren Johansen, Bent Nielsen
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2023 · Volume 85 · Issue 3
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 h 1 / 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.
Keywords
leverage, least median of squares estimator, outliers, regression, robust statistics
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