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.
@article{1013203456,
author = {Di Bucchianico, Alessandro and Einmahl, John H. and Mushkudiani, Nino A.},
title = {Smallest nonparametric tolerance regions},
journal = {Ann. Statist.},
volume = {29},
number = {2},
year = {2001},
pages = { 1320-1343},
language = {en},
url = {http://dml.mathdoc.fr/item/1013203456}
}
Di Bucchianico, Alessandro; Einmahl, John H.; Mushkudiani, Nino A. Smallest nonparametric tolerance regions. Ann. Statist., Tome 29 (2001) no. 2, pp. 1320-1343. http://gdmltest.u-ga.fr/item/1013203456/