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THE DISTANCE STANDARD DEVIATION
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DOI：10.1214/19-AOS1935.png)
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摘要
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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.
Keyword:
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
期刊
IF:
3.7
论文数:
2.8K
被引数:
2.9W
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引用论文
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PREAI
分享收藏EQUIVALENCE OF DISTANCE-BASED AND RKHS-BASED STATISTICS IN HYPOTHESIS TESTING.png)
ANNALS OF STATISTICS
OAAI
ANNALS OF STATISTICSIF3.7
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