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The minimum weighted covariance determinant estimator for high-dimensional data

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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.

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Acknowledgements

The research was supported by the projects GA21-05325S and GA19-05704S of the Czech Science Foundation. The authors would like to thank Jurjen Duintjer Tebbens for discussion, and would like to thank the anonymous referees, an associate editor, and the editor-in-chief for their time and constructive advice.

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Authors and Affiliations

  1. The Czech Institute of Sciences, Institute of Computer Science, Prague 8, Czech Republic

    Jan Kalina & Jan Tichavský

  2. The Czech Institute of Sciences, Institute of Information Theory and Automation, Prague 8, Czech Republic

    Jan Kalina

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  1. Jan Kalina
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  2. Jan Tichavský
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Correspondence to Jan Kalina.

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Kalina, J., Tichavský, J. The minimum weighted covariance determinant estimator for high-dimensional data. Adv Data Anal Classif 16, 977–999 (2022). https://doi.org/10.1007/s11634-021-00471-6

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