Testing Structural Hypotheses for the Copula: a Proofreading based on Functional Decomposition - Archive ouverte HAL
Article Dans Une Revue REVSTAT - Statistical Journal Année : 2024

Testing Structural Hypotheses for the Copula: a Proofreading based on Functional Decomposition

Résumé

Tests of multivariate independence may rely on asymptotically independent Cram\'er-von Mises statistics derived from a M\"obius 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.
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Dates et versions

hal-03905791 , version 1 (19-12-2022)
hal-03905791 , version 2 (08-03-2023)
hal-03905791 , version 3 (23-08-2023)

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  • HAL Id : hal-03905791 , version 3

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Cécile Mercadier. Testing Structural Hypotheses for the Copula: a Proofreading based on Functional Decomposition. REVSTAT - Statistical Journal, 2024. ⟨hal-03905791v3⟩
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