Dependence structure estimation using Copula Recursive Trees

Abstract

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 denisty 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 applications on simulated data.

Publication
Journal of Multivariate Analysis
Oskar Laverny
Oskar Laverny
Actuary - P.h.d

My research interests include dependences structures in high dimensions, copulas, code and actuarial sciences.

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