A0167
Title: Local moment matching with Gamma mixtures under automatic smoothness penalization
Authors: Oskar Laverny - Aix-Marseille Université (France) [presenting]
Philippe Lambert - Universite de Liege / Universite catholique de Louvain (Belgium)
Abstract: The class of Erlang mixture has been widely used in the literature for flexible density estimation procedures. More specifically, we consider them for the task of density estimation on the positive real line when the only available information is given as localized moments, such as a histogram with potentially higher-order moments in some bins. By construction, the obtained moment problem is ill-posed and requires regularization. Several penalties can be used for such a task, such as a lasso penalty for the sparsity of the representation, but we focus here on a simplified smoothness penalty coming from the P-splines literature. We show that the corresponding hyperparameter can be selected without cross-validation through the computation of the so-called effective dimension of the estimator, which makes the estimator practical and adapted to these summarized information settings. The flexibility of the local moments representations allows interesting additions, such as enforcing Value-at-Risk and Tail Value-at-Risk constraints on the resulting estimator, making the procedure fit for heavy-tailed estimations.
