The complexity of computing the MCD-estimator

T. Bernholt, Paul Fischer

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    In modem statistics the robust estimation of parameters is a central problem, i.e., an estimation that is not or only slightly affected by outliers in the data. The minimum covariance determinant (MCD) estimator (J. Amer. Statist. Assoc. 79 (1984) 871) is probably one of the most important robust estimators of location and scatter. The complexity of computing the MCD, however, was unknown and generally thought to be exponential even if the dimensionality of the data is fixed.

    Here we present a polynomial time algorithm for MCD for fixed dimension of the data. In contrast we show that computing the MCD-estimator is NP-hard if the dimension varies. (C) 2004 Elsevier B.V. All rights reserved.
    Original languageEnglish
    JournalTheoretical Computer Science
    Volume326
    Issue number1-3
    Pages (from-to)383-398
    ISSN0304-3975
    DOIs
    Publication statusPublished - 2004

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