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Last passage times of minimum contrast estimators

Part of: Distribution theory Stochastic analysis Parametric inference Limit theorems

Published online by Cambridge University Press:  09 April 2009

Arup Bose  and
Snigdhansu Chatterjee
Arup Bose
Affiliation:
Theoretical Statistics and Mathematics Unit Indian Statistical Institute203 B. T. Road Calcutta 700 035India e-mail: [email protected]
Snigdhansu Chatterjee
Affiliation:
Department of Mathematics The University of ManchesterOxford Road Manchester M139PLUK e-mail: [email protected]
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Abstract

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We study the last passage time and its asymptotic distribution for minimum contrast estimators defined through the minimization of a convex criterion function based on U-functionals. This includes cases of non-smooth estimators for vector valued parameters. We also derive a Bahadur-type representation and the law of iterated logarithms for such estimators.

Keywords

minimum contrast estimatorslast passage timelaw of iterated logarithmsBahadur representationOja medianL1median

MSC classification

Secondary: 62F12: Asymptotic properties of estimators 60F99: None of the above, but in this section 60H99: None of the above, but in this section 62E20: Asymptotic distribution theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 1 , August 2001 , pp. 1 - 10
Copyright
Copyright © Australian Mathematical Society 2001

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