An Adaptive Efficient Test for Gumbel Domain of Attraction

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 kn largest observations, for the Gumbel domain of attraction. Efficiency is achieved along certain contiguous extreme value alternatives within the concept of local asymptotic normal- ity (LAN). Simulations exemplify the results.

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