Some New Multivariate Tests of Independence

S. Bouzebda

We introduce some new nonparametic tests of independence which are functionals of the modified multivariate empirical copula process. In this work we extend the modified empirical process of Nikitin and Sporysheva (2009), which is defined by using a family of Gaussian processes of Deheuvels (2007b) to the multivariate case. The limiting behavior of the proposed statistics is established under the null hypothesis. Emphasis is placed on explanation of the strong approximation methodology.

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