Dependence calibration in conditional copulas: a nonparametric approach.
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.
Acar
Elif F
EF
Department of Statistics, University of Toronto, Toronto, Ontario M5S 3G3, Canada. elif@utstat.toronto.edu
Craiu
Radu V
RV
Yao
Fang
F
D000704:Analysis of Variance; D002138:Calibration; D003198:Computer Simulation; D009099:Multiple Birth Offspring; D018401:Sample Size; D013223:Statistics as Topic