General tests of independence based on empirical processes indexed by functions

作者：Bouzebda Salim^*

来源：Statistical Methodology, 2014, 21: 59-87.

DOI：10.1016/j.stamet.2014.03.001

• Empirical process
• Exchangeability
• Multivariate empirical copula processes
• Tests of independence
• Gaussian approximation
• Contiguous alternatives
• Mobius decomposition
• Half-spaces
• Cramer-von Mises statistic

The present paper is mainly concerned with the statistical tests of the independence problem between random vectors. We develop an approach based on general empirical processes indexed by a particular class of functions. We prove two abstract approximation theorems that include some existing results as particular cases. Finally, we characterize the limiting behavior of the Mobius transformation of empirical processes indexed by functions under contiguous sequences of alternatives.

• 出版日期2014-11