Abstract:
We consider main approaches to asymptotic testing hypotheses on
distributions when only k maximal order statistics of a sample are
observed. We assume that $k\to\infty$ and $k=o(n)$ where $n$ is
the sample size. A general criterion for a distribution tail
belonging to one of two classes is suggested provided all tails
from one of the classes are lighter than the tails from another
one. Further, we consider a problem of distinguish a simple
hypothesis on a distribution tail and a close (contigual)
alternative, and evaluate the limit distribution of the
corresponding likelihood ratio.