论文标题
依赖性结构使用副层递归树
Dependence structure estimation using Copula Recursive Trees
论文作者
论文摘要
我们构建了副层递归树（Cort）估计器：一个柔性，一致的，分段的线性估计器，利用Patchwork copula形式化和各种分段恒定密度估计器。尽管拼布结构强加了一个网格，但Cort估计器是数据驱动的，并从数据中递归地构造（可能是不规则的）网格，从而最大程度地减少了Copula空间上所选的距离。 Copula约束的添加使通常的密度估计器无法使用，而Cort估计器仅关注依赖性并保证边缘的均匀性。通过模拟数据开发，分析和测试了诸如局部尺寸降低和包装之类的改进。
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.
