Title: Copula-based multivariate expectile regression
Authors: Karim Oualkacha - UQAM (Canada) [presenting]
Aziz Lmoudden - UQAM (Canada)
Taoufik Bouezmarni - Universite de Sherbrooke (Canada)
Abstract: Expectiles summarize a distribution in a manner similar to quantiles. Expectile regression has recently gained great popularity, in part due to its attractive statistical and computational properties. Unfortunately, despite the renewed interest, it remains limited to single-output problems. To enhance this and gain insight into multivariate data, we build on a class of multivariate expectile loss functions to develop a unified and flexible copula-based multivariate expectile regression framework. Our approach provides a new class of multiple-output expectile regression estimators, which are unique solutions to convex risk minimization problems. We model the joint distribution of the multiple-output and the regressors using a copula model, which separates modelling the dependence and the marginal distributions. Then, we rewrite the multivariate expectile regression loss function in terms of the copula and the marginal distributions. We prove the asymptotic properties of our estimators (weak convergence and i.i.d. representation). We demonstrate the effectiveness of our approach through simulation studies and by analyzing the Fourth Dutch Growth data.