New Measure of the Bivariate Asymmetry

Autor(es)

Bahraoui, Tarik ; Kolev, Nikolai

• Tipo de documento: Artigo Científico
• Fonte: SANKHYA-SERIES A-MATHEMATICAL STATISTICS AND PROBABILITY; v. 83, n. 1, p. 28-pg., 2020-03-20.

Resumo

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)

• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 18/05262-7 - Estudos de Estruturas de Dependência por meio de Função Characterística de Cópula
• Beneficiário: Tarik Bahraoui
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado