@MISC{Wu07onthe, author = {Angela Y. Wu}, title = {On the Least Trimmed Squares Estimator}, year = {2007} }

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Abstract

The linear least trimmed squares (LTS) estimator is a statistical technique for estimating the line (or generally hyperplane) of fit for a set of points. It was proposed by Rousseeuw as a robust alternative to the classical least squares estimator. Given a set of n points in R d, in classical least squares the objective is to find a linear model (that is, nonvertical hyperplane) that minimizes the sum of squared residuals. In LTS the objective is to minimize the sum of the smallest 50 % squared residuals. LTS is a robust estimator with a 50%-breakdown point, which means that the estimator is insensitive to corruption due to outliers, provided that the outliers constitute less than 50 % of the set. LTS is closely related to the well known LMS estimator, in which the objective is to minimize the median squared residual, and LTA, in which the objective is to minimize the sum of the smallest 50 % absolute residuals. LTS has the advantage of being statistically more efficient than LMS. Unfortunately, the computational complexity of LTS is less well understood than LMS. In this paper we present new algorithms, both exact and approximate, for computing the LTS estimator. We also present hardness results for exact and approximate LTS and LTA.