Dependence Calibration in Conditional Copulas: A Nonparametric Approach

作者：Acar Elif F^*; Craiu Radu V; Yao Fang

来源：Biometrics, 2011, 67(2): 445-453.

DOI：10.1111/j.1541-0420.2010.01472.x

• Copula parameter
• Copula selection
• Covariate adjustment
• Local likelihood
• Local polynomials
• Prediction error

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.

• 出版日期2011-6