CORT : the Copula Recursive Tree

CORT : the Copula Recursive Tree

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Leveraging from the patchwork copula formalization and from various piecewise constant density estimators (minimum-distance based, tree-shaped, Bayesian partitioning, Delaunay tree, Voronoi histogram), we derive a flexible, consistent, piecewise constant estimator for a copula density. While the patchwork structure usually imposes the grid, our estimator is data-driven and construct the (possibly irregular) grid recursively from the data, minimizing a chosen distance on the copula space. Furthermore, while the addition of the copula constraints makes the available solutions for density estimation unusable, our estimator is only concerned with dependence and takes care of the uniformity of the margins. Refinements such as localized dimension reduction, bagging and boosting are developed, analyzed, and tested through application on simulated and real data.

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