Additive models for extremal quantile regression with Pareto-type distributions

Abstract

Estimating conditional quantiles in the tail of a distribution is an important problem for several applications. However, data sparsity indicates that the predictions of tail behavior are more difficult compared with those for the mean or center quantiles, in particular, when a multivariate covariate is used. As additive models are known to be an efficient approach for multiple regression, this study considers an additive model for extremal quantile regression. The conditional quantile function is first estimated using a two-stage estimation method for the intermediate-order (not too extreme) quantile. Subsequently, the extreme-order quantile estimator is constructed by extrapolating from the intermediate-order quantile estimator. By combining the asymptotic and extreme value theories, the theoretical properties of the intermediate- and extreme-order quantile estimators are evaluated. A simulation study is conducted to confirm the performance of the estimators, and an application using real data is provided.