THE DISTANCE STANDARD DEVIATION

被引：8

作者：

Edelmann, Dominic ^{[1
]}

Richards, Donald ^{[2
]}

Vogel, Daniel ^{[3
]}

机构：

[1] German Canc Res Ctr, Heidelberg, Germany

[2] Penn State Univ, Dept Stat, University Pk, PA 16802 USA

[3] Univ Aberdeen, Inst Complex Syst & Math Biol, Aberdeen, Scotland

来源：

ANNALS OF STATISTICS | 2020年 / 48卷 / 06期

关键词：

Asymptotic efficiency; characteristic function; dispersive ordering; distance correlation coefficient; distance variance; Gini's mean difference; measure of spread; order statistic; sample spacing; stochastic ordering; U-statistic; DEPENDENCE; INDEPENDENCE;

D O I：

10.1214/19-AOS1935

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：3395 / 3416

页数：22

共 43 条

[1]

[Anonymous], 2003, METRON INT J STAT

[2]

[Anonymous], 2016, THESIS

[3] Statistical properties of the |S| multivariate control chart. [J].