Non-parametric weighted tests for independence based on empirical copula process

Abstract

We propose a class of flexible non-parametric tests for the presence of dependence between components of a random vector based on weighted Cramér-von Mises functionals of the empirical copula process. The weights act as a tuning parameter and are shown to significantly influence the power of the test, making it more sensitive to different types of dependence. Asymptotic properties of the test are stated in the general case, for an arbitrary bounded and integrable weighting function, and computational formulas for a number of weighted statistics are provided. Several issues relating to the choice of the weights are discussed, and a simulation study is conducted to investigate the power of the test under a variety of dependence alternatives. The greatest gain in power is found to occur when weights are set proportional to true deviations from independence copula.

A Test for Independence Via Bayesian Nonparametric Estimation of Mutual Information

“…Additional tests of independence that count on mutual information can be found in Wu et al (2009), Mathew (2013) and Pethel and Hahs (2014). For other strategies of tests of independence such as copula process, distance covariance, and etc; see, Genest and Rémillard (2004), Kojadinovic and Holmes (2009), Medovikov (2016), Belalia et al (2017), Susam and Ucer (2018), Karvanen (2005), Meintanis and Iliopoulos (2008), Gaißer et al (2010), andFan et al (2017) for a comprehensive review. Roy et al (2019, pp.…”

A Bayesian Semiparametric Gaussian Copula Approach to a Multivariate Normality Test

“…Recent procedures tackling this problem can be found in Kim and Park (2018), Madukaife and Okafor (2018), Henze and Visagie (2019) and Al-Labadi et al (2019a). We highlight that, while most available works in the area of the hypothesis testing using copula approaches are related to assess independence (Genest and Rémillard, 2004;Kojadinovic and Holmes, 2009;Medovikov, 2016;Belalia et al, 2017), the proposed test is Bayesian and considers modeling the dependence structure and the marginal behaviors of the data separately to assess the multivariate normality assumption. Briefly, all univariate marginal distributions of F true are assumed to have the Dirichlet process to define posterior-based and prior-based models of F true .…”