Second-order regular variation, convolution and the central limit theorem
AbstractSecond-order regular variation is a refinement of the concept of regular variation which is useful for studying rates of convergence in extreme value theory and asymptotic normality of tail estimators. For a distribution tail 1 - F which possesses second-order regular variation, we discuss how this property is inherited by 1 - F2 and 1 - F*2. We also discuss the relationship of central limit behavior of tail empirical processes, asymptotic normality of Hill's estimator and second-order regular variation.
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 69 (1997)
Issue (Month): 2 (September)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
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- Jaap Geluk & Liang Peng & Casper G. de Vries, 1999. "Convolutions of Heavy Tailed Random Variables and Applications to Portfolio Diversification and MA(1) Time Series," Tinbergen Institute Discussion Papers 99-088/2, Tinbergen Institute.
- Necir, Abdelhakim & Meraghni, Djamel, 2009. "Empirical estimation of the proportional hazard premium for heavy-tailed claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 49-58, August.
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