Dependence Calibration in Conditional Copulas: A Nonparametric Approach
Article first published online: 23 AUG 2010
© 2010, The International Biometric Society
Volume 67, Issue 2, pages 445–453, June 2011
How to Cite
Acar, E. F., Craiu, R. V. and Yao, F. (2011), Dependence Calibration in Conditional Copulas: A Nonparametric Approach. Biometrics, 67: 445–453. doi: 10.1111/j.1541-0420.2010.01472.x
- Issue published online: 20 JUN 2011
- Article first published online: 23 AUG 2010
- Received September 2009. Revised May 2010. Accepted May 2010.
- Copula parameter;
- Copula selection;
- Covariate adjustment;
- Local likelihood;
- Local polynomials;
- Prediction error
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.