Title: Lasso and Dantzig selector for Bernstein copula
Authors: Artem Prokhorov - University of Sydney (Australia) [presenting]
Abstract: The LASSO and Dantzig selector are traditionally used for point estimation and model selection, especially within least squares problems where the number of parameters may exceed the number of observations. These methods are proposed to be used to regularise Bernstein copula based MLE problems. Besides offering a computationally efficient penalised estimator of the Bernstein copula, we consider estimation of the parameters in a correctly specified marginal distribution using the information in the copula. We show that the sparsity imposed by the regularisations is innocuous with respect to the non-asymptotic behavior of the sieve MLE, while it permits a substantial increase in computational efficiency compared to the unrestricted sieve MLE. We also study the parameter path behavior over a feasible range of tolerance levels and consider a version of the double Dantzig selector which resolves the arbitrariness in choosing the tolerance.