Dispersion of categorical variables and penalty functions: Derivation, estimation, and comparability

Zvi Gilula, Shelby J. Haberman

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

Measures of dispersion for categorical random variables based on penalty functions play a central role in establishing relevant measures of association between such variables. The literature concerning these measures provides little systematic treatment of such aspects of these measures as comparability, efficient estimation, and large-sample properties. This article provides a systematic and rigorous construction of dispersion measures based on penalty functions. Efficient estimation procedures and asymptotic properties of estimates are examined. Conditions from majorization theory that ensure a meaningful comparability of dispersion measures based on penalty functions are discussed. A large class of familiar dispersion measures is then given a new interpretation using these conditions.

Original languageEnglish
Pages (from-to)1447-1452
Number of pages6
JournalJournal of the American Statistical Association
Volume90
Issue number432
DOIs
StatePublished - Dec 1995

Keywords

  • Concentration
  • Entropy
  • Goodman–Kruskal measures
  • Majorization
  • Stochastic order

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