## The Annals of Statistics

### Some Poset Statistics

Paul R. Rosenbaum

#### 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.

#### Article information

Source
Ann. Statist., Volume 19, Number 2 (1991), 1091-1097.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176348141

Digital Object Identifier
doi:10.1214/aos/1176348141

Mathematical Reviews number (MathSciNet)
MR1105865

Zentralblatt MATH identifier
0729.62045

JSTOR