New Measure of the Bivariate Asymmetry

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Author(s):	Bahraoui, Tarik ; Kolev, Nikolai Total Authors: 2
Document type:	Journal article
Source:	SANKHYA-SERIES A-MATHEMATICAL STATISTICS AND PROBABILITY; v. 83, n. 1, p. 28-pg., 2020-03-20.
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. (AU)

FAPESP's process:	13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
Grantee:	Francisco Louzada Neto
Support Opportunities:	Research Grants - Research, Innovation and Dissemination Centers - RIDC


FAPESP's process:	18/05262-7 - Dependence Structure Studies via Copula Characteristic Function Approach
Grantee:	Tarik Bahraoui
Support Opportunities:	Scholarships in Brazil - Post-Doctoral