High-Breakdown Estimators of Multivariate Location and Scatter View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2013

AUTHORS

Peter Rousseeuw , Mia Hubert

ABSTRACT

This contribution gives a brief summary of robust estimators of multivariate location and scatter. We assume that the original (uncontaminated) data follow an elliptical distribution with location vector μ and positive definite scatter matrix Σ. Robust methods aim to estimate μ and Σ even though the data has been contaminated by outliers. The well-known multivariate M-estimators can break down when the outlier fraction exceeds 1/(p+1) where p is the number of variables. We describe several robust estimators that can withstand a high fraction (up to 50 %) of outliers, such as the minimum covariance determinant estimator (MCD), the Stahel–Donoho estimator, S-estimators and MM-estimators. We also discuss faster methods that are only approximately equivariant under linear transformations, such as the orthogonalized Gnanadesikan–Kettenring estimator and the deterministic MCD algorithm. More... »

PAGES

49-66

References to SciGraph publications

  • 2012-09. A comparison of algorithms for the multivariate L1-median in COMPUTATIONAL STATISTICS
  • 2002-04. Small sample corrections for LTS and MCD in METRIKA
  • 1985. Multivariate Estimation with High Breakdown Point in MATHEMATICAL STATISTICS AND APPLICATIONS
  • Book

    TITLE

    Robustness and Complex Data Structures

    ISBN

    978-3-642-35493-9
    978-3-642-35494-6

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-642-35494-6_4

    DOI

    http://dx.doi.org/10.1007/978-3-642-35494-6_4

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1033766049


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