On a class of stopping times for M-estimators

Winfried Stute

Journal of Multivariate Analysis, 1984, vol. 14, issue 1, 83-93

Abstract: For a given score function [psi] = [psi](x, [theta]), let [theta]n be Huber's M-estimator for an unknown population parameter [theta]. Under some mild smoothness assumptions it is known that n1/2([theta]n - [theta]) is asymptotically normal. In this paper the stopping times [tau]c(m) = inf{n >= m: n1/2 [theta]n - [theta] > c } associated with the sequence of confidence intervals for [theta] are investigated. A useful representation of M-estimators is derived, which is also appropriate for proving laws of the iterated logarithm and Donskertype invariance principles for ([pi]n)n.

Keywords: M-estimator; stopping; time; representation; law; of; the; iterated; logarithm; invariance; principle (search for similar items in EconPapers)
Date: 1984
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