JSM 2004 - Toronto

Abstract #301454

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Activity Number: 180
Type: Topic Contributed
Date/Time: Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
Sponsor: General Methodology
Abstract - #301454
Title: Optimal Distribution-free Confidence Bands for a Continuous CDF
Author(s): Jesse Frey*+
Companies: Ohio State University
Address: Dept. of Statistics, Columbus, OH, 43210,
Keywords: confidence bands ; ranked-set sampling ; Kolmogorov-Smirnov confidence bands
Abstract:

Distribution-free confidence bands for a cumulative distribution function are typically found through inversion of a distribution-free hypothesis test. We propose an alternative strategy in which the upper and lower bounds of the confidence band are chosen to minimize a weighted width criterion. We derive necessary and sufficient conditions for a confidence band to be optimal with respect to such a criterion, and we demonstrate that optimal bands are unique in most cases of practical interest. We apply our alternative strategy to the construction of confidence bands both for the case of simple random sampling and for the case of ranked-set sampling. Our confidence bands in the ranked-set sampling case condition on the observed sequence of order statistics. For that case, the computation of coverage probabilities is made possible by a new algorithm which does not seem to have any competitors in the literature.

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