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Small Sample Corrections for LTS and MCD

In: Developments in Robust Statistics

Author

Listed:
  • G. Pison

    (Universitaire Instelling Antwerpen (UIA), Department of Mathematics and Computer Science)

  • S. Van Aelst

    (Universitaire Instelling Antwerpen (UIA), Department of Mathematics and Computer Science)

  • G. Willems

    (Universitaire Instelling Antwerpen (UIA), Department of Mathematics and Computer Science)

Abstract

Summary The least trimmed squares estimator and the minimum covariance determinant estimator Rousseeuw (1984) are frequently used robust estimators of regression and of location and scatter. Consistency factors can be computed for both methods to make the estimators consistent at the normal model. However, for small data sets these factors do not make the estimator unbiased. Based on simulation studies we therefore construct formulas which allow us to compute small sample correction factors for all sample sizes and dimensions without having to carry out any new simulations. We give some examples to illustrate the effect of the correction factor.

Suggested Citation

  • G. Pison & S. Van Aelst & G. Willems, 2003. "Small Sample Corrections for LTS and MCD," Springer Books, in: Rudolf Dutter & Peter Filzmoser & Ursula Gather & Peter J. Rousseeuw (ed.), Developments in Robust Statistics, pages 330-343, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-57338-5_29
    DOI: 10.1007/978-3-642-57338-5_29
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