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General tests of independence based on empirical processes indexed by functions
Affiliation:1. Basic Science School, Changchun University of Technology, Changchun, China;2. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China;3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China;1. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China;2. School of Mathematics and Information Science, Shangqiu Normal University, Shangqiu 476000, China;3. School of data science, Zhejiang University of Finance and Economics, Hangzhou 310018, China;1. University Cergy-Pontoise, Mathematics, office E 5.28, UCP site Saint-Martin, 2 Bd. Adolphe Chauvin, 95000 Cergy-Pontoise, France;2. Aix-Marseille University, Campus de Luminy, 13288 Marseille cedex 9, France;1. Vilnius University, Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania;2. Université de Nantes, 1, quai de Tourville BP, Nantes Cedex 1, Nantes, 44313, France;1. School of Business, Universidad Francisco Marroquín, Calle Manuel F. Ayau, 01010, Ciudad de Guatemala, Guatemala;2. Department of Economics, Universidad Carlos III de Madrid, Calle Madrid 126, 28903, Getafe (Madrid), Spain
Abstract: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 Möbius transformation of empirical processes indexed by functions under contiguous sequences of alternatives.
Keywords:Empirical process  Exchangeability  Multivariate empirical copula processes  Tests of independence  Gaussian approximation  Contiguous alternatives  Möbius decomposition  Half-spaces  Cramér–von Mises statistic
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