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Exact iterative computation of the robust multivariate minimum volume ellipsoid estimator

Author

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  • Cook, R. D.
  • Hawkins, D. M.
  • Weisberg, S.

Abstract

A widely used procedure for robust estimation of the scatter matrix of multivariate data is the 'minimum volume ellipsoid' or MVE estimator. This seeks to find the ellipsoid of minimum volume which covers at least half of the data. Not only is the MVE used in its own right, it is also the starting point for most other high breakdown estimators of multivariate location and scatter. To date however, no exact algorithm for computing the MVE has been defined. This deficiency makes the MVE method, and all other methods using the MVE as a starting point, irreproducible. This paper gives an exact algorithm for computing the MVE and uses this exact algorithm to evaluate the performance of the approximate algorithm currently used in most MVE implementations.

Suggested Citation

  • Cook, R. D. & Hawkins, D. M. & Weisberg, S., 1993. "Exact iterative computation of the robust multivariate minimum volume ellipsoid estimator," Statistics & Probability Letters, Elsevier, vol. 16(3), pages 213-218, February.
    • Handle: RePEc:eee:stapro:v:16:y:1993:i:3:p:213-218
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    Citations

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    Cited by:

    1. Selin Ahipaşaoğlu, 2015. "Fast algorithms for the minimum volume estimator," Journal of Global Optimization, Springer, vol. 62(2), pages 351-370, June.
    2. J. L. Alfaro & J. Fco. Ortega, 2009. "A comparison of robust alternatives to Hotelling's T2 control chart," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(12), pages 1385-1396.
    3. Hawkins, Douglas M., 1995. "Convergence of the feasible solution algorithm for least median of squares regression," Computational Statistics & Data Analysis, Elsevier, vol. 19(5), pages 519-538, May.
    4. Pronzato, Luc, 2003. "Removing non-optimal support points in D-optimum design algorithms," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 223-228, July.
    5. Beirlant, J. & Mason, D. M. & Vynckier, C., 1999. "Goodness-of-fit analysis for multivariate normality based on generalized quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 30(2), pages 119-142, April.
    6. Croux, Christophe & Haesbroeck, Gentiane, 1997. "An easy way to increase the finite-sample efficiency of the resampled minimum volume ellipsoid estimator," Computational Statistics & Data Analysis, Elsevier, vol. 25(2), pages 125-141, July.
    7. Hawkins, Douglas M. & Olive, David J., 1999. "Improved feasible solution algorithms for high breakdown estimation," Computational Statistics & Data Analysis, Elsevier, vol. 30(1), pages 1-11, March.

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