2023/08/23 by Cécile Mercadier, Mercadier, Cécile
Computer Science · #Fuzzy Logic and Control Systems #Mathematics, Computing, and Information Processing #Natural Language Processing Techniques #copula models #functional decomposition #idempotent maps #rank-based inference
paper · pdf · doi:10.57805/revstat.vi.675
openalex publication_date 2023/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Tests of multivariate independence may rely on asymptotically independent Cramérvon Mises statistics derived from a Möbius decomposition of the empirical copula process. We generalize this approach to some other copula-based assumptions, with the help of a functional decomposition based on commuting idempotent maps. As soon as the null hypothesis reflects the stability of the copula under the action of the composition of such operators, the methodology applies. The empirical testing process, which depends on the decomposition, allows the derivation of a new family of test statistics. The asymptotic distributions are obtained. Since the latter depend on the unknown copula being tested, we adapt parametric bootstrap or subsampling procedure to our setting to approximate p-values. The benefits in deriving test statistics from a functional decomposition are illustrated and discussed through simulations.