Optimal distribution-free confidence bands for a distribution function.

Distribution-free confidence bands for a distribution function are typically obtained by inverting a distribution-free hypothesis test. We propose an alternate strategy in which the upper and lower bounds of the confidence band are chosen to minimize a narrowness criterion. We derive necessary and sufficient conditions for optimality with respect to such a criterion, and we use these conditions to construct an algorithm for finding optimal bands. We also derive uniqueness results, with the Brunn-Minkowski Inequality from the theory of convex bodies playing a key role in this work. We illustrate the optimal confidence bands using some galaxy velocity data, and we also show that the optimal bands compare favorably to other bands both in terms of power and in terms of area enclosed.

Main Author: Frey, Jesse.
Language: English
Published: 2008
Online Access: http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:176382
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dc_source_str_mv Journal of Statistical Planning and Interference, 2008.
author Frey, Jesse.
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author_s Frey, Jesse.
spellingShingle Frey, Jesse.
Optimal distribution-free confidence bands for a distribution function.
author-letter Frey, Jesse.
author_sort_str Frey, Jesse.
dc_title_str Optimal distribution-free confidence bands for a distribution function.
title Optimal distribution-free confidence bands for a distribution function.
title_short Optimal distribution-free confidence bands for a distribution function.
title_full Optimal distribution-free confidence bands for a distribution function.
title_fullStr Optimal distribution-free confidence bands for a distribution function.
title_full_unstemmed Optimal distribution-free confidence bands for a distribution function.
collection_title_sort_str optimal distribution-free confidence bands for a distribution function.
title_sort optimal distribution-free confidence bands for a distribution function.
description Distribution-free confidence bands for a distribution function are typically obtained by inverting a distribution-free hypothesis test. We propose an alternate strategy in which the upper and lower bounds of the confidence band are chosen to minimize a narrowness criterion. We derive necessary and sufficient conditions for optimality with respect to such a criterion, and we use these conditions to construct an algorithm for finding optimal bands. We also derive uniqueness results, with the Brunn-Minkowski Inequality from the theory of convex bodies playing a key role in this work. We illustrate the optimal confidence bands using some galaxy velocity data, and we also show that the optimal bands compare favorably to other bands both in terms of power and in terms of area enclosed.
publishDate 2008
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fgs.label Optimal distribution-free confidence bands for a distribution function.
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dc.title Optimal distribution-free confidence bands for a distribution function.
dc.creator Frey, Jesse.
dc.description Distribution-free confidence bands for a distribution function are typically obtained by inverting a distribution-free hypothesis test. We propose an alternate strategy in which the upper and lower bounds of the confidence band are chosen to minimize a narrowness criterion. We derive necessary and sufficient conditions for optimality with respect to such a criterion, and we use these conditions to construct an algorithm for finding optimal bands. We also derive uniqueness results, with the Brunn-Minkowski Inequality from the theory of convex bodies playing a key role in this work. We illustrate the optimal confidence bands using some galaxy velocity data, and we also show that the optimal bands compare favorably to other bands both in terms of power and in terms of area enclosed.
dc.date 2008
dc.identifier vudl:176382
dc.source Journal of Statistical Planning and Interference, 2008.
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