The multivariate least-trimmed squares estimator

By José Julio Espina Agulló, Christophe Croux, S. Van Aelst. 2008

118 citations recorded by the source corpus.

In this paper we introduce the least-trimmed squares estimator for multivariate regression. We give three equivalent formulations of the estimator and obtain its breakdown point. A fast algorithm for its computation is proposed. We prove Fisher-consistency at the multivariate regression model with elliptically symmetric error distribution and derive the influence function. Simulations investigate the finite-sample efficiency and robustness of the estimator. To increase the efficiency of the estimator, we also consider a one-step reweighted estimator.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/80e3040aea26bd11659e79e79ac03d9f8a2c17ac

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In Statistics and Probability

Citations in the corpus

High-Breakdown Robust Multivariate Methods (2008, background): “Depthbased estimators have been proposed and studied by Donoho and Gasko (1992), Rousseeuw, Ruts and Tukey (1999a), Liu, Parelius and Singh (1999), Zuo and Serfling (2000a, 2000b) and Zuo, Cui and He (2004).”
Central limit theorem and influence function for the MCD estimators at general multivariate distributions (2009, background): “These estimators, in particular the covariance estimator, also serve as robust plug-ins in other multivariate statistical techniques, such as principal component analysis [6, 21], multivariate linear regression [1, 20], discriminant analysis [11], factor analysis [16], canonical correlations [22, 25”
Outlier detection for high-dimensional data (2015, background): “It is usually required that m(Y) < h (Agulló et al., 2008).”