Testing for Positive Quadrant Dependence. Issue 1 (21st January 2021)

• Record Type: Journal Article
• Authors: Tang, Chuan-Fa; Wang, Dewei; El Barmi, Hammou; Tebbs, Joshua M.
• Is Part Of: American statistician. Volume 75:Issue 1(2021)
• Page Start: 23
• Page End: 30
• Publication Date: 2021-01-21
• Subjects: Bivariate data -- Copula function -- Empirical likelihood -- Independence -- Kendall's rank test -- Spearman's rank test; Statistics -- Periodicals; 001.42205
• DOI: 10.1080/00031305.2019.1607554
• Languages: English
• ISSNs: 0003-1305

Abstract

Abstract: We develop an empirical likelihood (EL) approach to test independence of two univariate random variables X and Y versus the alternative that X and Y are strictly positive quadrant dependent (PQD). Establishing this type of ordering between X and Y is of interest in many applications, including finance, insurance, engineering, and other areas. Adopting the framework in Einmahl and McKeague, we create a distribution-free test statistic that integrates a localized EL ratio test statistic with respect to the empirical joint distribution of X and Y . When compared to well-known existing tests and distance-based tests we develop by using copula functions, simulation results show the EL testing procedure performs well in a variety of scenarios when X and Y are strictly PQD. We use three datasets for illustration and provide an online R resource practitioners can use to implement the methods in this article. Supplementary materials for this article are available online.