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Recent results on asymptotic expansions in extreme-value theory

Sweeting, TJ; (1989) Recent results on asymptotic expansions in extreme-value theory. In: Husler, J and Reiss, R-D, (eds.) Extreme value theory. (pp. 10 - 20). Springer: Germany.

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Abstract

We present an overview of some current work on asymptotic expansions in extreme value theory. It is shown that in the case of local convergence the problem of obtaining an asymptotic expansion for the quantile function amounts to that of finding an expansion for the integral of a regularly varying function. The class of regularly varying functions of differentiable order k is introduced, and it is shown how one can develop expansions for such functions. Asymptotic expansions for distribution functions can in principle be obtained by inversion; in particular, we give conditions for the validity of the formal expansion of Uzgoren (1954) for the case F in D(λ).

Type:Proceedings paper
Title:Recent results on asymptotic expansions in extreme-value theory
Event:Oberwolfach Meeting on Extreme Value Theory
Location:Oberwolfach, Germany
Dates:1987-12-06 - 1987-12-12
ISBN:0387969543
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science

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