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On the Computation of Symmetrized M-Estimators of Scatter

In: Recent Advances in Robust Statistics: Theory and Applications

Author

Listed:
  • Jari Miettinen

    (University of Jyvaskyla, Department of Mathematics and Statistics)

  • Klaus Nordhausen

    (University of Turku, Department of Mathematics and Statistics
    University of Tampere, School of Health Sciences)

  • Sara Taskinen

    (University of Jyvaskyla, Department of Mathematics and Statistics)

  • David E. Tyler

    (Rutgers University, Department of Statistics)

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.

Suggested Citation

  • Jari Miettinen & Klaus Nordhausen & Sara Taskinen & David E. Tyler, 2016. "On the Computation of Symmetrized M-Estimators of Scatter," Springer Books, in: Claudio Agostinelli & Ayanendranath Basu & Peter Filzmoser & Diganta Mukherjee (ed.), Recent Advances in Robust Statistics: Theory and Applications, pages 151-167, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-3643-6_8
    DOI: 10.1007/978-81-322-3643-6_8
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