We construct a flexible, consistent, piecewise linear estimator for a copula, leveraging the patchwork copula formalization and various piecewise constant density estimators. While the patchwork structure imposes the grid, our estimator is data-driven and constructs the 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 guarantees the uniformity of margins. Refinements such as localised dimension reduction and bagging are developed, analyzed, and tested through applications on simulated data.
This conference was virtual, and filmed ! The video is online if you want.