On model selection in the case of nested distributions — An application to frailty models

A number of criteria, test statistics and diagnostic plots have been developed in order to test the adapted distribution assumption. Usually, a simpler distribution is tested against a more complicated one (by adding an extra parameter), which include the first distribution as a special case (nested distributions). In this paper, two new tests are developed in order to test nested distributions. This work concentrates on the case where the extra parameter lies on the boundary of the parameter space. The developed tests are applied on testing the frailty term on frailty models. Simulation results are presented for comparison with other test statistics and the methods are illustrated on two real data sets.