3907
1993
eng
article
1
2010-04-26
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Von Mises condition revisited
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.
urn:nbn:de:bvb:20-opus-45790
4579
In: The Annals of Probability (1993) 21, 3, 1310 - 1328
Michael Falk
Frank Marohn
eng
uncontrolled
Von Mises conditions
eng
uncontrolled
extreme value theory
eng
uncontrolled
extreme value distribution
eng
uncontrolled
extreme order statistics
eng
uncontrolled
generalized Pareto distribution
Mathematik
open_access
Institut für Mathematik
Universität Würzburg
https://opus.bibliothek.uni-wuerzburg.de/files/3907/Marohn_Mises_condition.pdf
3908
1994
eng
article
1
2010-04-26
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On statistical information of extreme order statistics, local extreme value alternatives, and Poisson point processes
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.
urn:nbn:de:bvb:20-opus-45816
4581
In: Journal of Multivariate Analysis (1994) 48, 1, 1- 30
A. Janssen
Frank Marohn
Mathematik
open_access
Institut für Mathematik
Universität Würzburg
https://opus.bibliothek.uni-wuerzburg.de/files/3908/Marohn_Statistical_information.pdf
3911
1993
eng
article
1
2010-04-27
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Asymptotically optimal tests for conditional distributions
No abstract available
urn:nbn:de:bvb:20-opus-45823
4582
In: The Annals of Statistics (1993) 21, 1, 45 - 60
Michael Falk
Frank Marohn
Mathematik
Point processes
Asymptotic distribution theory
Order statistics; empirical distribution functions
open_access
Institut für Mathematik
Universität Würzburg
https://opus.bibliothek.uni-wuerzburg.de/files/3911/Marohn_Asymptotic_tests.pdf
3912
1994
eng
article
1
2010-04-27
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Asymptotic sufficiency of order statistics for almost regular Weibull type densities
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.
urn:nbn:de:bvb:20-opus-45837
4583
In: Statistics & Decisions, 1994, 12, 385 - 393
Frank Marohn
eng
uncontrolled
Weibull type density
eng
uncontrolled
intermediate order statistics
eng
uncontrolled
asymptotic sufficiency
eng
uncontrolled
local asymptotic normality
Mathematik
Order statistics; empirical distribution functions
open_access
Institut für Mathematik
Universität Würzburg
https://opus.bibliothek.uni-wuerzburg.de/files/3912/Marohn_Asymptotic_sufficiency.pdf
3914
1991
deu
article
1
2010-05-20
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Global sufficiency of extreme order statistics in location models of Weibull type
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.
urn:nbn:de:bvb:20-opus-47874
4787
In: Probability Theory and Related Fields (1991) 88, 261-268
Frank Marohn
deu
swd
Extremwertstatistik
deu
swd
Weibull-Verteilung
Mathematik
Order statistics; empirical distribution functions
open_access
Institut für Mathematik
Universität Würzburg
https://opus.bibliothek.uni-wuerzburg.de/files/3914/Marohn_Global_sufficiency.pdf