Large sample behaviour of some well-known robust estimators under long-range dependence

Abstract

This paper concerns robust location and scale estimators under long-range dependence, focusing on the Hodges–Lehmann location estimator, on the Shamos–Bickel scale estimator and on the Rousseeuw–Croux scale estimator. The large sample properties of these estimators are reviewed. This paper includes computer simulation in order to examine how well the estimators perform at finite sample sizes.

Keywords:

• long-range dependence
• U-process
• Hodges–Lehmann location estimator
• Bickel–Shamos scale estimator
• Croux–Rousseeuw scale estimator
• Ma–Genton autocovariance estimator

Acknowledgements

M.S.T. would like to thank Telecom ParisTech for their hospitality. This research was partially supported by the NSF Grant DMS-0706786 at Boston University. \noindent V.A.R. would like to thank Telecom ParisTech for their hospitality and CNPq-Brazil for financial support. \noindent Dedication: We would like to dedicate this paper to Benoit Mandelbrot, who led the way.