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June, 1991 Some Poset Statistics
Paul R. Rosenbaum
Ann. Statist. 19(2): 1091-1097 (June, 1991). DOI: 10.1214/aos/1176348141

Abstract

Statistics or functions are discussed that measure agreement between certain types of partially ordered data. These poset statistics are a generalization of two familiar classes of functions: the arrangement increasing functions and the decreasing reflection functions; those functions measure agreement between linearly ordered data. Specifically, the statistics in question are functions $h(\mathbf{X}_1, \mathbf{X}_2)$ of two matrix arguments, each having $N$ rows and they measure the agreement of the ordering of the $N$ rows of the two matrices. An example is used to illustrate and motivate the discussion. One statistic in this class is applied to the example; it generalizes Wilcoxon's rank sum statistic, Spearman's rank correlation and Page's statistic for ordered alternatives.

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Paul R. Rosenbaum. "Some Poset Statistics." Ann. Statist. 19 (2) 1091 - 1097, June, 1991. https://doi.org/10.1214/aos/1176348141

Information

Published: June, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0729.62045
MathSciNet: MR1105865
Digital Object Identifier: 10.1214/aos/1176348141

Subjects:
Primary: 62G10
Secondary: 06A10 , 20P05

Keywords: arrangement increasing function , decreasing in transposition , decreasing reflection function , partial order , rank tests , Reflection group

Rights: Copyright © 1991 Institute of Mathematical Statistics

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Vol.19 • No. 2 • June, 1991
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