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

• 成果类型: Article
• 署名作者: Gilula, Z; Haberman, SJ
• 署名单位: University of Chicago; Northwestern University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2291537
• 发表日期: 1995
• 页码: 1447-1452
• 关键词: association

摘要

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.