Fast Algorithms for Computing High Breakdown Covariance Matrices with Missing Data

Hubert, M., Pison, G., Struyf, A., Van Aelst, S., THEORY AND APPLICATIONS OF RECENT ROBUST METHODS, p. 71-82, Basel: Birkhauser, 2004

13 Pages Posted: 17 Feb 2011

See all articles by Samuel Copt

Samuel Copt

affiliation not provided to SSRN

Maria-Pia Victoria-Feser

University of Geneva - HEC

Date Written: February 17, 2004

Abstract

Robust estimation of covariance matrices when some of the data at hand are missing is an important problem. It has been studied by Little and Smith (1987) and more recently by Cheng and Victoria-Feser (2002). The latter propose the use of high breakdown estimators and so-called hybrid algorithms (see, e.g., Woodruff and Rocke, 1994). In particular, the minimum volume ellipsoid of Rousseeuw (1984) is adapted to the case of missing data. To compute it, they use (a modified version of) the forward search algorithm (see e.g. Atkinson, 1994). In this paper, we propose to use instead a modification of the C-step algorithm proposed by Rousseeuw and Van Driessen (1999) which is actually a lot faster. We also adapt the orthogonalized Gnanadesikan-Kettenring (OGK) estimator proposed by Maronna and Zamar (2002) to the case of missing data and use it as a starting point for an adapted S-estimator. Moreover, we conduct a simulation study to compare different robust estimators in terms of their efficiency and breakdown.

Keywords: C-step algorithm, minimum covariance determinant, outliers, robust statistics, S-estimators, orthogonalized Gnanadesikan-Kettering robust estimator

Suggested Citation

Copt, Samuel and Victoria-Feser, Maria-Pia, Fast Algorithms for Computing High Breakdown Covariance Matrices with Missing Data (February 17, 2004). Hubert, M., Pison, G., Struyf, A., Van Aelst, S., THEORY AND APPLICATIONS OF RECENT ROBUST METHODS, p. 71-82, Basel: Birkhauser, 2004, Available at SSRN: https://ssrn.com/abstract=1763232

Samuel Copt

affiliation not provided to SSRN ( email )

Maria-Pia Victoria-Feser (Contact Author)

University of Geneva - HEC ( email )

40 Boulevard du Pont d'Arve
Geneva 4, Geneva 1211
Switzerland

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