On hypothesis tests in misspecified change-point problems for a Poisson process |
| |
Authors: | Christian Farinetto |
| |
Institution: | Laboratoire de Statistique et Processus, Université du Maine, Le Mans, Cedex 9, France |
| |
Abstract: | Consider an inhomogeneous Poisson process X on 0, T] whose unk-nown intensity function “switches” from a lower function g* to an upper function h* at some unknown point ?* that has to be identified. We consider two known continuous functions g and h such that g*(t) ? g(t) < h(t) ? h*(t) for 0 ? t ? T. We describe the behavior of the generalized likelihood ratio and Wald’s tests constructed on the basis of a misspecified model in the asymptotics of large samples. The power functions are studied under local alternatives and compared numerically with help of simulations. We also show the following robustness result: the Type I error rate is preserved even though a misspecified model is used to construct tests. |
| |
Keywords: | Change-point type problem GLRT inhomogeneous Poisson process misspecified model Wald’s test |
|
|