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Inequalities for the relative sufficiency between sets of order statistics. (English) Zbl 0583.62039

Statistical extremes and applications, Proc. NATO Adv. Study Inst., Vimeiro/Port. 1983, NATO ASI Ser., Ser. C 131, 597-610 (1984).
[For the entire collection see Zbl 0542.00013.]
The authors obtain a refinement of a result due to L. Weiss [Ann. Stat. 2, 795-802 (1974; Zbl 0284.62019)] concerning the asymptotic sufficiency of a relatively small number of order statistics in tests of fit testing the hypothesis that a sample is drawn from a completely specified distribution P. Some extensions, useful in cases where one is only interested in local properties of the distribution P, such as quantiles or the density function at a certain quantile, is also considered.
Reviewer: R.Helmers

MSC:

62G10 Nonparametric hypothesis testing
62G30 Order statistics; empirical distribution functions
62B05 Sufficient statistics and fields