We construct the COpula Recursive Tree (CORT) estimator: a flexible, consistent, piecewise linear estimator of a copula, leveraging the patchwork copula formalization and various piecewise constant density estimators. While the patchwork structure imposes a grid, the CORT estimator is data-driven and constructs the (possibly irregular) grid recursively from the data, minimizing a chosen distance on the copula space. The addition of the copula constraints makes usual density estimators unusable, whereas the CORT estimator is only concerned with dependence and guarantees the uniformity of margins. Refinements such as localized dimension reduction and bagging are developed, analyzed, and tested through simulated data.

我们构建了 COpula 递归树 (CORT) 估计器：一个灵活的、一致的、分段线性估计器，利用了拼凑的 copula 形式化和各种分段常数密度估计器。虽然拼凑结构强加了一个网格，但 CORT 估计器是数据驱动的，并从数据中递归构建（可能是不规则的）网格，从而最小化 copula 空间上的选定距离。copula 约束的添加使得通常的密度估计器无法使用，而 CORT 估计器仅关注相关性并保证边缘的均匀性。通过模拟数据开发、分析和测试局部降维和装袋等改进。