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October 2001 Smallest nonparametric tolerance regions
Alessandro Di Bucchianico, John H. Einmahl, Nino A. Mushkudiani
Ann. Statist. 29(5): 1320-1343 (October 2001). DOI: 10.1214/aos/1013203456


We present a new, natural way to construct nonparametric multivariate tolerance regions. Unlike the classical nonparametric tolerance intervals, where the endpoints are determined by beforehand chosen order statistics, we take the shortest interval that contains a certain number of observations. We extend this idea to higher dimensions by replacing the class of intervals by a general class of indexing sets, which specializes to the classes of ellipsoids, hyperrectangles or convex sets.The asymptotic behavior of our tolerance regions is derived using empirical process theory, in particular the concept of generalized quantiles. Finite sample properties of our tolerance regions are investigated through a simulation study. Real data examples are also presented.


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Alessandro Di Bucchianico. John H. Einmahl. Nino A. Mushkudiani. "Smallest nonparametric tolerance regions." Ann. Statist. 29 (5) 1320 - 1343, October 2001.


Published: October 2001
First available in Project Euclid: 8 February 2002

zbMATH: 1043.62045
MathSciNet: MR1873333
Digital Object Identifier: 10.1214/aos/1013203456

Primary: 60F05 , 62G15 , 62G20 , 62G30

Keywords: asymptotic normality , empirical process , minimum volume set , Nonparametric tolerance region , prediction region

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 5 • October 2001
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