Dependence Calibration in Conditional Copulas: A Nonparametric Approach

• Published in: Biometrics 2011-06, Vol.67 (2), p.445-453
• Main Authors: Acar, Elif F., Craiu, Radu V., Yao, Fang
• Format: Article
• Language: English
• Subjects: Analysis of Variance; Bioinformatics; BIOMETRIC METHODOLOGY; Biometrics; Calibration; Computer Simulation; Copula functions; Copula parameter; Copula selection; Covariate adjustment; Estimation bias; Estimators; Gestational age; Local likelihood; Local polynomials; Mathematical independent variables; Multiple Birth Offspring; Parametric models; Polynomials; Prediction error; Sample Size; Statistics as Topic; Twins; Variance analysis
• ISSN: 0006-341X; 1541-0420
• DOI: 10.1111/j.1541-0420.2010.01472.x

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.