Dependence Calibration in Conditional Copulas: A Nonparametric Approach

Summary The study of dependence between random variables is a mainstay in statistics. In many cases, the strength of dependence between two or more random variables varies according to the values of a measured covariate. We propose inference for this type of variation using a conditional copula model where the copula function belongs to a parametric copula family and the copula parameter varies with the covariate. In order to estimate the functional relationship between the copula parameter and the covariate, we propose a nonparametric approach based on local likelihood. Of importance is also the choice of the copula family that best represents a given set of data. The proposed framework naturally leads to a novel copula selection method based on cross‐validated prediction errors. We derive the asymptotic bias and variance of the resulting local polynomial estimator, and outline how to construct pointwise confidence intervals. The finite‐sample performance of our method is investigated using simulation studies and is illustrated using a subset of the Matched Multiple Birth data.