Second-order regular variation, convolution and the central limit theorem
Second-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.
Year of publication: |
1997
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Authors: | Geluk, J. ; de Haan, L. ; Resnick, S. ; Starica, C. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 69.1997, 2, p. 139-159
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Publisher: |
Elsevier |
Keywords: | Regular variation Second-order behavior Tail empirical measure Extreme value theory Convolution Maxima Hill estimator |
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