TY  - JOUR
A1  - Falk, Michael
A1  - Marohn, Frank
T1  - Von Mises condition revisited
N2  - It is shown that the rate of convergence in the von Mises conditions of extreme value theory determines the distance of the underlying distribution function F from a generalized Pareto distribution. The distance is measured in terms of the pertaining densities with the limit being ultimately attained if and only if F is ultimately a generalized Pareto distribution. Consequently, the rate of convergence of the extremes in an lid sample, whether in terms of the distribution of the largest order statistics or of corresponding empirical truncated point processes, is determined by the rate of convergence in the von Mises condition. We prove that the converse is also true.
KW  - Von Mises conditions
KW  - extreme value theory
KW  - extreme value distribution
KW  - extreme order statistics
KW  - generalized Pareto distribution
Y1  - 1993
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-45790
ER  - 
TY  - JOUR
A1  - Janssen, A.
A1  - Marohn, Frank
T1  - On statistical information of extreme order statistics, local extreme value alternatives, and Poisson point processes
N2  - The aim of the present paper is to clarify the role of extreme order statistics in general statistical models. This is done within the general setup of statistical experiments in LeCam's sense. Under the assumption of monotone likelihood ratios, we prove that a sequence of experiments is asymptotically Gaussian if, and only if, a fixed number of extremes asymptotically does not contain any information. In other words: A fixed number of extremes asymptotically contains information iff the Poisson part of the limit experiment is non-trivial. Suggested by this result, we propose a new extreme value model given by local alternatives. The local structure is described by introducing the space of extreme value tangents. It turns out that under local alternatives a new class of extreme value distributions appears as limit distributions. Moreover, explicit representations of the Poisson limit experiments via Poisson point processes are found. As a concrete example nonparametric tests for Frechet type distributions against stochastically larger alternatives are treated. We find asymptotically optimal tests within certain threshold models.
Y1  - 1994
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-45816
ER  - 
TY  - JOUR
A1  - Falk, Michael
A1  - Marohn, Frank
T1  - Asymptotically optimal tests for conditional distributions
N2  - No abstract available
Y1  - 1993
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-45823
ER  - 
TY  - JOUR
A1  - Marohn, Frank
T1  - Asymptotic sufficiency of order statistics for almost regular Weibull type densities
N2  - Consider a location family which is defined via a Weibull type density having shape parameter a = 1. We treat the problem, which portion of the order statistics is asymptotically sufficient. It turns out that the intermediate order statistics are relevant.
KW  - Weibull type density
KW  - intermediate order statistics
KW  - asymptotic sufficiency
KW  - local asymptotic normality
Y1  - 1994
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-45837
ER  - 
TY  - JOUR
A1  - Marohn, Frank
T1  - Global sufficiency of extreme order statistics in location models of Weibull type
N2  - In Janssen and Reiss (1988) it was shown that in a location model of a Weibull type sample with shape parameter -1 < a < 1 the k(n) lower extremes are asymptotically local sufficient. In the present paper we show that even global sufficiency holds. Moreover, it turns out that convergence of the given statistical experiments in the deficiency metric does not only hold for compact parameter sets but for the whole real line.
KW  - Extremwertstatistik
KW  - Weibull-Verteilung
Y1  - 1991
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-47874
ER  -