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An Adaptive Efficient Test for Gumbel Domain of Attraction
Author(s) -
Marohn Frank
Publication year - 1998
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00105
Subject(s) - gumbel distribution , mathematics , extreme value theory , generalized extreme value distribution , attraction , independent and identically distributed random variables , asymptotic distribution , scale (ratio) , domain (mathematical analysis) , scale parameter , nuisance parameter , local asymptotic normality , normality test , statistics , distribution (mathematics) , value (mathematics) , statistical hypothesis testing , mathematical analysis , random variable , linguistics , philosophy , physics , quantum mechanics , estimator
We consider n independent observations, generated identically by some distribution function, which belongs to the domain of attraction of an extreme value distribution with unknown shape and scale parameter. We treat the scale parameter as a nuisance parameter and establish an adaptive efficient test sequence, which is based on the k n largest observations, for the Gumbel domain of attraction. Efficiency is achieved along certain contiguous extreme value alternatives within the concept of local asymptotic normality (LAN). Simulations exemplify the results