A simple general approach to inference about the tail of a distribution. (English) Zbl 0323.62033

Hill, Bruce M.

Ann. Stat. 3, 1163-1174 (1975).

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