Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

We present several parameter estimation problems dealing with situations when the model depends on the unknown parameter in a non-regular way. The problems correspond to observations of different natures, but all have the same type of singularity: a cusp. We will see that all the considered models give rise to the same limiting likelihood ratio process. So, it seems that (like the regular case and unlike the case of change-point type singularity) the limiting likelihood ratio process is universal in presence of a cusp type singularity.