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Fast algorithms for computing high breakdown covariance matrices with missing data

Authors
Copt, Samuel
Published in Hubert, M., Pison, G., Struyf, A. and Van Aelst, S. Theory and Applications of Recent Robust Methods. Basel: Birkhauser. 2004, p. 71-82
Collection Statistics for Industry and Technology Series
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 algorithmMinimum covariance determinantOutliersRobust statisticsS-estimatorsOrthogonalized Gnanadesikan-Kettering robust estimator
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COPT, Samuel, VICTORIA-FESER, Maria-Pia. Fast algorithms for computing high breakdown covariance matrices with missing data. In: Hubert, M., Pison, G., Struyf, A. and Van Aelst, S. (Ed.). Theory and Applications of Recent Robust Methods. Basel : Birkhauser, 2004. p. 71-82. (Statistics for Industry and Technology Series) https://archive-ouverte.unige.ch/unige:6502

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Deposited on : 2010-05-04

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