A model where the least trimmed squares estimator is maximum likelihood
<p>The least trimmed squares (LTS) estimator is a popular robust regression estimator. It finds a subsample of <em>h</em> ‘good’ observations among <em>n</em> observations and applies least squares on that subsampl...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Wiley
2023
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| Summary: | <p>The least trimmed squares (LTS) estimator is a popular robust regression estimator. It finds a subsample of <em>h</em> ‘good’ observations among <em>n</em> 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 <em>h</em> ‘good’, normal observations. The LTS estimator is found to be <em>h</em><sup>1/2</sup> consistent and asymptotically standard normal in the location-scale case. Consistent estimation of <em>h</em> is discussed. The model differs from the commonly used <em>ϵ</em>-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.</p> |
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