Second order regular variation and its applications to rates of convergence in extreme-value distribution
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The rate of convergence of the distribution of order statisticsto the corresponding extreme-value distribution may be characterized bythe uniform and total variation metrics. de Haan and Resnick [4] de-rived the convergence rate when the second order generalized regularlyvarying function has second order derivatives. In this paper, based on theproperties of the generalized regular variation and the second order gener-alized variation and characterized by uniform and total variation metrics,the convergence rates of the distribution of the largest order statistic areobtained under weaker conditions.
Abstract
The rate of convergence of the distribution of order statisticsto the corresponding extreme-value distribution may be characterized bythe uniform and total variation metrics. de Haan and Resnick [4] de-rived the convergence rate when the second order generalized regularlyvarying function has second order derivatives. In this paper, based on theproperties of the generalized regular variation and the second order gener-alized variation and characterized by uniform and total variation metrics,the convergence rates of the distribution of the largest order statistic areobtained under weaker conditions.
참고문헌 (7)
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- L. de Haan, "On regular variation and its application to the weak convergence of sample extremes" (1970), Mathematisch Centrum
- L. de Haan, "Second-order regular variation and rates of convergence in extreme-value theory", Annals of Probability, 24(1), pp.97~ (1996)
- L. de Haan, "Generalized regular variation of second order", Journal of the Australian Mathematical Society Series A, 61(3), pp.381~395 (1996)
- B. V. Gnedenko, "Sur la distribution limite du terme maximum d’ne serie aleatoire", Annals of Mathematics, 44, pp.423~453 (1943)
- S. Nadarajah, "Extreme value theory, models and simulation, Stochastic processes: mod-elling and simulation", Handbook of Statistics, 21, pp.607~691 (2003)