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On estimation of the exponent of regular variation using a sample with missing observations

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  • Mladenovic, Pavle
  • Piterbarg, Vladimir

Abstract

Let (Xn) be a sequence of possibly dependent random variables with the same marginal distribution function F, such that 1-F(x)=x-[alpha]L(x), [alpha]>0, where L(x) is a slowly varying function. In this paper the Hill estimator of the exponent of regular variation based on a sample with missing observations from the sequence (Xn) is considered. The asymptotic consistency was proved under some general conditions. This extends results of Hsing [1991. On tail index estimation using dependent data. Ann. Statist. 19, 1547-1569].

Suggested Citation

  • Mladenovic, Pavle & Piterbarg, Vladimir, 2008. "On estimation of the exponent of regular variation using a sample with missing observations," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 327-335, March.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:4:p:327-335
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    Cited by:

    1. Ilić, Ivana, 2012. "On tail index estimation using a sample with missing observations," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 949-958.

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