Book chapter
Open access

Fast algorithms for computing high breakdown covariance matrices with missing data

Published inTheory and Applications of Recent Robust Methods, Editors Hubert, M., Pison, G., Struyf, A. and Van Aelst, S., p. 71-82
PublisherBasel : Birkhauser
  • Statistics for Industry and Technology Series
Publication date2004

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.

  • C-step algorithm
  • Minimum covariance determinant
  • Outliers
  • Robust statistics
  • S-estimators
  • Orthogonalized Gnanadesikan-Kettering robust estimator
Citation (ISO format)
COPT, Samuel, VICTORIA-FESER, Maria-Pia. Fast algorithms for computing high breakdown covariance matrices with missing data. In: Theory and Applications of Recent Robust Methods. Basel : Birkhauser, 2004. p. 71–82. (Statistics for Industry and Technology Series)
Main files (1)
Book chapter
  • PID : unige:6502

Technical informations

Creation04/30/2010 4:09:00 PM
First validation04/30/2010 4:09:00 PM
Update time03/14/2023 3:28:44 PM
Status update03/14/2023 3:28:44 PM
Last indexation08/28/2023 5:59:45 PM
All rights reserved by Archive ouverte UNIGE and the University of GenevaunigeBlack