On the efficiency of Gini's mean difference

DOI10.1007/s10260-015-0315-xzbMath1328.62299arXiv1405.5027OpenAlexW1889598023MaRDI QIDQ897849

Carina Gerstenberger, Daniel Vogel

Publication date: 8 December 2015

Published in: Statistical Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.5027

zbMATH Keywords

robustnessinfluence functionstandard deviationresidue theoremmean deviation\(Q_n\)median absolute deviationnormal mixture distribution

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric robustness (62G35) Nonparametric estimation (62G05)

Related Items (11)

Gini heterogeneity index for detecting uncertainty in ordinal data surveys ⋮ A new control chart using GINI C_PK ⋮ Stochastic orders and measures of skewness and dispersion based on expectiles ⋮ Gini covariance matrix and its affine equivariant version ⋮ Estimation and confidence intervals of modified process capability index using robust measure of variability ⋮ Worst-case analysis of Gini mean difference safety measure ⋮ The distance standard deviation ⋮ TESTING FOR CHANGES IN KENDALL’S TAU ⋮ Gini's mean difference and variance as measures of finite populations scales ⋮ Tests for Scale Changes Based on Pairwise Differences ⋮ An asymptotic test for constancy of the variance under short-range dependence

Uses Software

• R
• robustbase

Cites Work

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• Limit theorems for the median deviation
• Expansions for statistics involving the mean absolute deviations
• Descriptive statistics for non-parametric models. III: Dispersion
• The mean and median absolute deviations
• Gini's mean difference: a superior measure of variability for non-normal distributions
• The Influence Curve and Its Role in Robust Estimation
• Alternatives to the Median Absolute Deviation
• THE STANDARD ERROR OF GINI'S MEAN DIFFERENCE
• A Class of Statistics with Asymptotically Normal Distribution
• The Standard Error of Gini's Mean Difference
• Robust Statistics

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