Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Law of the iterated logarithm and invariance principle for $ M$-estimators

Authors: Xuming He and Gang Wang
Journal: Proc. Amer. Math. Soc. 123 (1995), 563-573
MSC: Primary 62F35; Secondary 60F15, 60F17
MathSciNet review: 1231036
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Abstract: We prove the law of the iterated logarithm for a general class of M-estimators which covers in particular robust M-estimators and S-estimators of multivariate location-scatter. We also obtain an almost sure invariance principle (Bahadur-type representation) for these estimators.

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Keywords: Bahadur representation, invariance principle, law of the iterated logarithm, location-scatter, M-estimator, robustness, S-estimator
Article copyright: © Copyright 1995 American Mathematical Society