On the Computation of Symmetrized M-Estimators of Scatter
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.
KeywordsMaximum Likelihood Estimator Independent Component Analysis Pairwise Difference Multivariate Normal Distribution Scatter Matrix
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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