THE DISTANCE STANDARD DEVIATION

• 成果类型: Article
• 署名作者: Edelmann, Dominic; Richards, Donald; Vogel, Daniel
• 署名单位: Helmholtz Association; German Cancer Research Center (DKFZ); Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of Aberdeen
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1935
• 发表日期: 2020
• 页码: 3395-3416
• 关键词: dependence; INDEPENDENCE

摘要

The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption of finite second moments. Applications are provided to hypothesis testing on a data set from materials science and to multivariate statistical quality control. The distance standard deviation is compared to classical scale measures for inference on the spread of heavy-tailed distributions. Inequalities for the distance variance are derived, proving that the distance standard deviation is bounded above by the classical standard deviation and by Gini's mean difference. New expressions for the distance standard deviation are obtained in terms of Gini's mean difference and the moments of spacings of order statistics. It is also shown that the distance standard deviation satisfies the axiomatic properties of a measure of spread.