New Measure of the Bivariate Asymmetry

A new measure of the bivariate asymmetry of a dependence structure between two random variables is introduced based on copula characteristic function. The proposed measure is represented as the discrepancy between the rank–based distance correlation computed over two complementary order-preserved se...

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Bibliographic Details
Published in:Sankhya. Series. A 2021-02, Vol.83 (1), p.421-448
Main Authors: Bahraoui, Tarik, Kolev, Nikolai
Format: Article
Language:English
Subjects:
Mathematics and Statistics
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
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Summary:A new measure of the bivariate asymmetry of a dependence structure between two random variables is introduced based on copula characteristic function. The proposed measure is represented as the discrepancy between the rank–based distance correlation computed over two complementary order-preserved sets. General properties of the measure are established, as well as an explicit expression for the empirical version. It is shown that the proposed measure is asymptotically equivalent to a fourth–order degenerate V -statistics and that the limit distributions have representations in terms of weighted sums of an independent chi-square random variables. Under dependent random variables, the asymptotic behavior of bivariate distance covariance and variance process is demonstrated. Numerical examples illustrate the properties of the measures.
ISSN:0976-836X
0976-8378
DOI:10.1007/s13171-019-00197-w