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Computation of robust estimates of multivariate location and shape

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  • D. M. Rocke
  • D. L. Woodruff

Abstract

This paper reviews the state of the art in the computation of robust estimates of multivariate location and shape using combinatorial estimators such as the minimum volume ellipsoid (MVE) and iterative M‐ and S‐estimators. We also present new results on the behavior of M‐ and S‐estimators in the presence of different types of outliers, and give the first computational evidence on compound estimators that use the MVE as a starting point for an S‐estimator. Problems with too many data points in too many dimensions cannot be handled by any available technology; however, the methods presented in this paper substantially extend the size of problem that can be successfully handled.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:stanee:v:47:y:1993:i:1:p:27-42
    DOI: 10.1111/j.1467-9574.1993.tb01404.x
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    Cited by:

    1. 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.
    2. Christmann, A. & Van Aelst, S., 2006. "Robust estimation of Cronbach's alpha," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1660-1674, August.
    3. Kosinski, Andrzej S., 1998. "A procedure for the detection of multivariate outliers," Computational Statistics & Data Analysis, Elsevier, vol. 29(2), pages 145-161, December.

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