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, Volume 21, Issue 4, pp 697–729 | Cite as

Estimating an endpoint with high-order moments

  • Stéphane Girard
  • Armelle Guillou
  • Gilles Stupfler
Original Paper

Abstract

We present a new method for estimating the endpoint of a unidimensional sample when the distribution function decreases at a polynomial rate to zero in the neighborhood of the endpoint. The estimator is based on the use of high-order moments of the variable of interest. It is assumed that the order of the moments goes to infinity, and we give conditions on its rate of divergence to get the asymptotic normality of the estimator. The good performance of the estimator is illustrated on some finite sample situations.

Keywords

Endpoint estimation High-order moments Consistency Asymptotic normality 

Mathematics Subject Classification (2000)

62G32 62G05 

Notes

Acknowledgements

The authors are indebted to the anonymous referees for their helpful comments and suggestions that have contributed to an improved presentation of the results of this paper.

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2011

Authors and Affiliations

  • Stéphane Girard
    • 1
  • Armelle Guillou
    • 2
  • Gilles Stupfler
    • 2
  1. 1.Team Mistis, INRIA Rhône-Alpes & LJK, InovalléeSaint-Ismier cedexFrance
  2. 2.Université de Strasbourg & CNRS, IRMA, UMR 7501Strasbourg cedexFrance

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