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Robust covariance matrix estimation and multivariate outlier detection

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  • Peña, Daniel
  • Prieto, Francisco J.

Abstract

A severe limitation for the application of robust position and scale estimators having a high breakdown point is a consequence of their high computational cost. In this paper we present and analyze several inexpensive robust estimators for the co variance matrix, based on information obtained from projections onto certain sets of directions. The properties of these estimators (breakdown point, computational cost, bias) are analyzed and compared with those of the Stahel-Donoho estimator, through simulation studies. These studies show a clear improvement both on the computational requirements and the bias properties of the Stahel-Donoho estimator. The same ideas are also applied to the construction of procedures to detect outliers in multivariate samples. Their performance is analyzed by applying them to a set of test cases.

Suggested Citation

  • Peña, Daniel & Prieto, Francisco J., 1997. "Robust covariance matrix estimation and multivariate outlier detection," DES - Working Papers. Statistics and Econometrics. WS 10497, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:10497
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    References listed on IDEAS

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    1. N. A. Campbell, 1980. "Robust Procedures in Multivariate Analysis I: Robust Covariance Estimation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 231-237, November.
    2. Rousseeuw, Peter J., 1993. "A resampling design for computing high-breakdown regression," Statistics & Probability Letters, Elsevier, vol. 18(2), pages 125-128, September.
    3. D. M. Rocke & D. L. Woodruff, 1993. "Computation of robust estimates of multivariate location and shape," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 47(1), pages 27-42, March.
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    1. N. Locantore & J. Marron & D. Simpson & N. Tripoli & J. Zhang & K. Cohen & Graciela Boente & Ricardo Fraiman & Babette Brumback & Christophe Croux & Jianqing Fan & Alois Kneip & John Marden & Daniel P, 1999. "Robust principal component analysis for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 1-73, June.

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