  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.
