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A simple general approach to inference about the tail of a distribution. (English) Zbl 0323.62033
Summary: Let $$Y_1,\dots,Y_n$$, be a sample of independent random variables having a common distribution $$G$$, about which some partial information is available, but whose global form is unspecified. By conditioning upon an appropriate subset of the data (determined by a combination of theoretical and data-analytic methods) such a non-parametric problem can be reduced to a relatively tractable parametric form for which both Bayesian and non-Bayesian solutions are available. For example, of the partial information consists of knowledge of the upper tail behavior of the distribution, e.g. $$1-G(x)\sim Cx^{-\alpha}$$ for sufficiently large $$x$$, then conditioning upon certain of the large order statistics allows an extremely simple parametric analysis.
Reviewer: Bruce M. Hill

MSC:
 62G30 Order statistics; empirical distribution functions 62F99 Parametric inference
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