Non-nested hypothesis testing inference for GAMLSS models

Two or more regression models are said to be non-nested if neither can be obtained from the remaining models when parametric restrictions are imposed. Tests for choosing between linear non-nested regression models are found in literature, such as J and MJ tests. In this paper we propose variants of these two tests for the GAMLSS (Generalized Additive Models for Location, Scale and Shape) class of models. We report Monte Carlo evidence on finite sample behaviour of the proposed tests. Bootstrap-based testing inference is also considered. Overall, bootstrap MJ test had the best performance. An empirical application is presented and discussed.