Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator

• Published in: Journal of multivariate analysis Vol. 71; no. 2; pp. 161 - 190
• Main Authors: Croux, Christophe, Haesbroeck, Gentiane
• Format: Journal Article Web Resource
• Language: English
• Published: San Diego, CA Elsevier Inc 01.11.1999; Elsevier; Academic Press
• Series: Journal of Multivariate Analysis
• Subjects: Exact sciences and technology; influence function; influence function minimum covariance determinant estimator robust estimation scatter matrix; Linear inference, regression; Mathematics; Mathématiques; minimum covariance determinant estimator; Physical, chemical, mathematical & earth Sciences; Physique, chimie, mathématiques & sciences de la terre; Probability and statistics; robust estimation; scatter matrix; Sciences and techniques of general use; Statistics; minimum covariance determinant estimator; scatter matrix; influence function; robust estimation; Statistical regression; Influence function; Covariance analysis; Estimator robustness; Multivariate distribution; Dispersion matrix; Covariance matrix; Variance analysis
• ISSN: 0047-259X; 1095-7243; 1095-7243
• DOI: 10.1006/jmva.1999.1839

The minimum covariance determinant (MCD) scatter estimator is a highly robust estimator for the dispersion matrix of a multivariate, elliptically symmetric distribution. It is relatively fast to compute and intuitively appealing. In this note we derive its influence function and compute the asymptotic variances of its elements. A comparison with the one step reweighted MCD and with S-estimators is made. Also finite-sample results are reported.