On the Computation of Symmetrized M-Estimators of Scatter

Jari Miettinen (), Klaus Nordhausen (), Sara Taskinen () and David E. Tyler ()
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Jari Miettinen: University of Jyvaskyla, Department of Mathematics and Statistics
Klaus Nordhausen: University of Turku, Department of Mathematics and Statistics
Sara Taskinen: University of Jyvaskyla, Department of Mathematics and Statistics
David E. Tyler: Rutgers University, Department of Statistics

A chapter in Recent Advances in Robust Statistics: Theory and Applications, 2016, pp 151-167 from Springer

Abstract: 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.

Keywords: Maximum Likelihood Estimator; Independent Component Analysis; Pairwise Difference; Multivariate Normal Distribution; Scatter Matrix (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-81-322-3643-6_8

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