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