New Measure of the Bivariate Asymmetry

Tarik Bahraoui () and Nikolai Kolev ()
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Tarik Bahraoui: University of São Paulo
Nikolai Kolev: University of São Paulo

Sankhya A: The Indian Journal of Statistics, 2021, vol. 83, issue 1, No 18, 448 pages

Abstract: Abstract 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.

Keywords: Copula characteristic function; Degenerate V-statistics; Distance correlation; Rank statistics; Dependence measure; Asymmetry; Primary 62H20; 62G30; Secondary 60E10 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13171-019-00197-w

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