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On the Computation of Symmetrized M-Estimators of Scatter

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Recent Advances in Robust Statistics: Theory and Applications

Abstract

This paper focuses on the computational aspects of symmetrized M-estimators of scatter, i.e., the multivariate M-estimators of scatter computed on the pairwise differences of the data. Such estimators do not require a location estimate, and more importantly, they possess the important block and joint independence properties. These properties are needed, for example, when solving the independent component analysis problem. Classical and recently developed algorithms for computing the M-estimators and the symmetrized M-estimators are discussed. The effect of parallelization is considered as well as new computational approach based on using only a subset of pairwise differences. Efficiencies and computation time comparisons are made using simulation studies under multivariate elliptically symmetric models and under independent component models.

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Acknowledgments

This work was supported by the Academy of Finland under Grants 251965, 256291, and 268703. David Tyler’s work for this material was supported by the National Science Foundation under Grant No. DMS-1407751. We thank Dr. Seija Sirkiä for providing us the asymptotic relative efficiencies of the symmetrized estimators. The authors are grateful to the reviewers for their helpful comments.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Jyvaskyla, 40014, Jyvaskyla, Finland

    Jari Miettinen & Sara Taskinen

  2. Department of Mathematics and Statistics, University of Turku, 20014, Turku, Finland

    Klaus Nordhausen

  3. School of Health Sciences, University of Tampere, 30014, Tampere, Finland

    Klaus Nordhausen

  4. Department of Statistics, Rutgers University, New Brunswick, NJ, 08854, USA

    David E. Tyler

Authors
  1. Jari Miettinen
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  2. Klaus Nordhausen
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  3. Sara Taskinen
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  4. David E. Tyler
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Corresponding author

Correspondence to Jari Miettinen .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Trento, Trento, Italy

    Claudio Agostinelli

  2. Interdisciplinary Statistical Research Unit, Indian Statistical Institute, Kolkata, India

    Ayanendranath Basu

  3. Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria

    Peter Filzmoser

  4. Sampling and Official Statistics Unit, Indian Statistical Institute, Kolkata, India

    Diganta Mukherjee

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Miettinen, J., Nordhausen, K., Taskinen, S., Tyler, D.E. (2016). On the Computation of Symmetrized M-Estimators of Scatter. In: Agostinelli, C., Basu, A., Filzmoser, P., Mukherjee, D. (eds) Recent Advances in Robust Statistics: Theory and Applications. Springer, New Delhi. https://doi.org/10.1007/978-81-322-3643-6_8

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