A model where the least trimmed squares estimator is maximum likelihood

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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 E-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.
Original languageEnglish
JournalJournal of The Royal Statistical Society Series B-statistical Methodology
Issue number3
Pages (from-to)886-912
Publication statusPublished - 2023

    Research areas

  • leverage, least median of squares estimator, outliers, regression, robust statistics

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