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Rank-based inference tools for copula regression, with property and casualty insurance applications. (English) Zbl 1427.91223
Summary: Rank-based procedures are commonly used for inference in copula models for continuous responses whose behavior does not depend on covariates. This paper describes how these procedures can be adapted to the broader framework in which (possibly nonlinear) regression models for the marginal responses are linked by a copula that does not depend on covariates. The validity of many of these techniques can be derived from the asymptotic equivalence between the classical empirical copula process and its analog based on suitable residuals from the marginal models. Moment-based parameter estimation and copula goodness-of-fit tests are shown to remain valid under weak conditions on the marginal error term distributions, even when the residual-based empirical copula process fails to converge weakly. The performance of these procedures is evaluated through simulation in the context of two general insurance applications: micro-level multivariate insurance claims, and dependent loss triangles.
MSC:
91G05 Actuarial mathematics
62P05 Applications of statistics to actuarial sciences and financial mathematics
62H05 Characterization and structure theory for multivariate probability distributions; copulas
Software:
copula; copula; gcmr; R; simsalapar
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