The distance standard deviation

DOI10.1214/19-aos1935zbMath1462.62357arXiv1705.05777OpenAlexW3113308802MaRDI QIDQ85655

Donald Richards, Dominic Edelmann, Daniel Vogel, Daniel Vogel, Donald St. P. Richards, Dominic Edelmann

Publication date: 1 December 2020

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.05777

zbMATH Keywords

characteristic functionasymptotic efficiencyorder statisticstochastic orderingU-statisticGini's mean differencedispersive orderingdistance correlation coefficientmeasure of spreadsample spacingdistance variance

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Inequalities; stochastic orderings (60E15) Measures of association (correlation, canonical correlation, etc.) (62H20) Order statistics; empirical distribution functions (62G30) Characteristic functions; other transforms (60E10) Characterization and structure theory of statistical distributions (62E10)

Related Items (5)

A nonparametric test for comparing survival functions based on restricted distance correlation ⋮ A consistent version of distance covariance for right‐censored survival data and its application in hypothesis testing ⋮ A basic treatment of the distance covariance ⋮ dcortools ⋮ A regression perspective on generalized distance covariance and the Hilbert-Schmidt independence criterion

Uses Software

• energy
• multivariance
• dcortools

Cites Work

• Partial distance correlation with methods for dissimilarities
• Measuring and testing dependence by correlation of distances
• Ball Covariance: A Generic Measure of Dependence in Banach Space
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• The distance correlation \(t\)-test of independence in high dimension
• The affinely invariant distance correlation
• Distance correlation coefficients for Lancaster distributions
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• Brownian distance covariance
• DISCO analysis: A nonparametric extension of analysis of variance
• The Gini methodology. A primer on a statistical methodology.
• Gini's mean difference: a superior measure of variability for non-normal distributions
• Distance multivariance: new dependence measures for random vectors
• A generalization of an integral arising in the theory of distance correlation
• Measuring nonlinear dependence in time-series, a distance correlation approach
• Selected Works of E. L. Lehmann
• Asymptotic Statistics
• A Consistent Test for Bivariate Dependence
• Statistical properties of the lsi multivariate control chart
• Empirical Characteristic Functions‐Based Estimation and Distance Correlation for Locally Stationary Processes
• Jackknifing $U$-Statistics
• Nonparametric independence testing via mutual information
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