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The minimum weighted covariance determinant estimator for high-dimensional data

Author

Listed:
  • Jan Kalina

    (The Czech Institute of Sciences, Institute of Computer Science
    The Czech Institute of Sciences, Institute of Information Theory and Automation)

  • Jan Tichavský

    (The Czech Institute of Sciences, Institute of Computer Science)

Abstract

In a variety of diverse applications, it is very desirable to perform a robust analysis of high-dimensional measurements without being harmed by the presence of a possibly larger percentage of outlying measurements. The minimum weighted covariance determinant (MWCD) estimator, based on implicit weights assigned to individual observations, represents a promising and flexible extension of the popular minimum covariance determinant (MCD) estimator of the expectation and scatter matrix of mlutivariate data. In this work, a regularized version of the MWCD denoted as the minimum regularized weighted covariance determinant (MRWCD) estimator is proposed. At the same time, it is accompanied by an outlier detection procedure. The novel MRWCD estimator is able to outperform other available robust estimators in several simulation scenarios, especially in estimating the scatter matrix of contaminated high-dimensional data.

Suggested Citation

  • Jan Kalina & Jan Tichavský, 2022. "The minimum weighted covariance determinant estimator for high-dimensional data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(4), pages 977-999, December.
    • Handle: RePEc:spr:advdac:v:16:y:2022:i:4:d:10.1007_s11634-021-00471-6
    DOI: 10.1007/s11634-021-00471-6
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