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A Joint Confidence Region for a Ranking Based on Differences

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A Joint Confidence Region for a Ranking Based on Differences

Written by:
RRS2024-03
pdf DOWNLOAD RESEARCH REPORT SERIES (Statistics #2024-03) [<1.0 MB]

Abstract

Klein, Wright, and Wieczorek (2020), hereafter KWW, presents a simple novel measure of uncertainty for an estimated ranking by constructing a joint confidence region using overlapping intervals of separate population parameters θk for the (unknown) true ranking of K populations, k = 1; 2; … ; K. In this paper, we consider the same topic but construct a new joint confidence region using intervals for differences of population parameters of the type θk - θk’ where k ≠ k’. With this new approach and for each k and k’, we ask which such intervals overlap the number 0. We show a condition under which the new joint confidence region shows no greater uncertainty than the uncertainty of the KWW joint confidence region.

Page Last Revised - June 12, 2024
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