The minimum weighted covariance determinant estimator revisited

Abstract

This paper is devoted to robust estimation of parameters of multivariate data. It investigates the minimum weighted covariance determinant estimator, which is based on implicit weights assigned to individual observations and is highly resistant to the presence of outlying values (outliers). We propose alternative versions of the estimator, which can be computed by means of the same (approximate) algorithm. Based on numerical experiments, we recommend especially a version of the estimator based on minimizing the product of (only) several eigenvalues of the weighted covariance matrix of the data. This version is namely able to overcome the performance of several available estimators including MM-estimators on contaminated data. Another proposal with promising performance is a two-stage adaptive weighting scheme for the estimator.

Keywords:

• Consistency factor
• Implicit weighting
• Multivariate data
• Robustness
• Simulations

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H12
• 62G35

Acknowledgments

The author would like to thank Jan Tichavský for help with the computations and the referee for valuable advice.

Additional information

Funding

The research was supported by the project GA18-01137S of the Czech Science Foundation.