Transformation-Kernel Estimation of Copula Densities
针对标准核估计在连接函数密度估计中的边界偏差和不一致问题，提出一种改进的变换核估计方法，通过平滑锥化处理消除边界异常，并给出理论性质和参数选择方法，模拟和实例验证了其有效性。
The standard kernel estimator of copula densities suffers from boundary biases and inconsistency due to unbounded densities. Transforming the domain of estimation into an unbounded one remedies both problems, but also introduces an unbounded multiplier that may produce erratic boundary behaviors in the final density estimate. We propose an improved transformation-kernel estimator that employs a smooth tapering device to counter the undesirable influence of the multiplier. We establish the theoretical properties of the new estimator and its automatic higher-order improvement under Gaussian copulas. We present two practical methods of smoothing parameter selection. Extensive Monte Carlo simulations demonstrate the competence of the proposed estimator in terms of global and tail performance. Two real-world examples are provided. Supplementary materials for this article are available online.