Conditional copulas are useful tools for modeling the dependence between multiple response variables that may vary with a given set of predictor variables. Conditional dependence measures such as conditional Kendall's tau and Spearman's rho that can be expressed as functionals of the conditional copula are often used to evaluate the strength of dependence conditioning on the covariates. In general, semiparametric estimation methods of conditional copulas rely on an assumed parametric copula family where the copula parameter is assumed to be a function of the covariates. The functional relationship can be estimated nonparametrically using different techniques but it is required to choose an appropriate copula model from various candidate families. In this paper, by employing the empirical checkerboard Bernstein copula (ECBC) estimator we propose a fully nonparametric approach for estimating conditional copulas, which doesn't require any selection of parametric copula models. Closed-form estimates of the conditional dependence measures are derived directly from the proposed ECBC-based conditional copula estimator. We provide the large-sample consistency of the proposed estimator as well as the estimates of conditional dependence measures. The finite-sample performance of the proposed estimator and comparison with semiparametric methods are investigated through simulation studies. An application to real case studies is also provided.

翻译：条件连接函数是建模多个响应变量间依赖关系（可能随给定预测变量集变化）的有效工具。常用条件依赖度量（如条件Kendall秩相关系数τ和Spearman秩相关系数ρ）可表示为条件连接函数的泛函，用于评估协变量条件下的依赖强度。通常，条件连接函数的半参数估计方法依赖于假定的参数连接函数族，其中连接函数参数被假定为协变量的函数。该函数关系虽可通过不同技术进行非参数估计，但需从多个候选族中选择合适的连接函数模型。本文通过引入经验棋盘伯恩斯坦连接函数（ECBC）估计量，提出一种完全非参数的条件连接函数估计方法，无需选择任何参数连接函数模型。基于所提出的ECBC条件连接函数估计量，可直接推导出条件依赖度量的闭式估计。我们给出了所提估计量及条件依赖度量估计的大样本一致性。通过模拟研究考察了所提估计量的有限样本性能，并与半参数方法进行了比较。此外还提供了实际案例应用。