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

Xuming He; Gang Wang

doi:10.1090/S0002-9939-1995-1231036-7

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

Xuming He
, Gang Wang

Arts & Sciences

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We prove the law of the iterated logarithm for a general class of Mestimators 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.

Original language	English
Pages (from-to)	563-573
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	123
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1995-1231036-7
State	Published - Feb 1995

Keywords

Bahadur representation
Invariance principle
Law of the iterated logarithm
Location-scatter
M-estimator
Robustness
S-estimator

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10.1090/S0002-9939-1995-1231036-7

Cite this

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title = "Law of the iterated logarithm and invariance principle for M-estimators",

abstract = "We prove the law of the iterated logarithm for a general class of Mestimators 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.",

keywords = "Bahadur representation, Invariance principle, Law of the iterated logarithm, Location-scatter, M-estimator, Robustness, S-estimator",

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AU - He, Xuming

AU - Wang, Gang

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N2 - We prove the law of the iterated logarithm for a general class of Mestimators 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.

AB - We prove the law of the iterated logarithm for a general class of Mestimators 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.

KW - Bahadur representation

KW - Invariance principle

KW - Law of the iterated logarithm

KW - Location-scatter

KW - M-estimator

KW - Robustness

KW - S-estimator

UR - https://www.scopus.com/pages/publications/84966202120

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DO - 10.1090/S0002-9939-1995-1231036-7

M3 - Article

AN - SCOPUS:84966202120

SN - 0002-9939

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EP - 573

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -

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

Abstract

Keywords

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