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Statistical testing of covariate effects in conditional copula models. (English) Zbl 1280.62052
Summary: In conditional copula models, the copula parameter is deterministically linked to a covariate via the calibration function. The latter is of central interest for inference and is usually estimated nonparametrically. However, in many applications it is scientifically important to test whether the calibration function is constant or not. Moreover, a correct model of a constant relationship results in significant gains of statistical efficiency. We develop a methodology for testing a parametric formulation of the calibration function against a general alternative and propose a generalized likelihood ratio-type test that enables conditional copula model diagnostics. We derive the asymptotic null distribution of the proposed test and study its finite sample performance using simulations. The method is applied to two data examples.

62G10 Nonparametric hypothesis testing
62H20 Measures of association (correlation, canonical correlation, etc.)
62E20 Asymptotic distribution theory in statistics
65C60 Computational problems in statistics (MSC2010)
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