Sums of ranking differences and inversion numbers for method discrimination. (2nd May 2013)

• Record Type: Journal Article
• Authors: Koziol, James A.
• Is Part Of: Journal of chemometrics. Volume 27:Number 6(2013:Jun.)
• Page Start: 165
• Page End: 169
• Publication Date: 2013-05-02
• Subjects: sum of ranking differences -- inversion number -- permutations; Chemistry -- Mathematics -- Periodicals; Chemistry -- Statistical methods -- Periodicals; 542.85
• DOI: 10.1002/cem.2504
• Languages: English
• ISSNs: 0886-9383

Abstract

Abstract : Héberger and colleagues [ Trends Anal Chem 2010;29:101–109; J Chemometrics 2011;25:151–158] have introduced the sum of ranking differences as a measure for comparing models or methods and have demonstrated its applicability in a variety of settings. The sum of ranking differences is closely related to another distance measure for permutations, namely, the inversion number. In this note, we describe the inversion number along with some of its distributional properties and draw comparisons with the sum of ranking differences for model comparison. Copyright © 2013 John Wiley & Sons, Ltd. Abstract : Héberger and colleagues [ Trends Anal Chem 2010;29:101–109; J Chemometrics 2011;25:151–158] have introduced the sum of ranking differences as a measure for comparing models or methods and have demonstrated its applicability in a variety of settings. The sum of ranking differences is closely related to another distance measure for permutations, namely, the inversion number. In this note, we describe the inversion number along with some of its distributional properties and draw comparisons with the sum of ranking differences for model comparison.