ИСТИНА

Translation invariance is a typical property of limiting statistical experiments. The notion of a statistical experiment with independent increments was introduced by Strasser (1985). Such models often appear as limits in non-regular cases. Examples of statistical models where limiting experiments are translation invariant and have independent increments are numerous. For instance, one can mention i.i.d. observations with densities having jumps along some smooth lines and smooth elsewhere, different change-point type models, threshold autoregressive processes. In this talk we provide a full description of translation invariant models with independent increments and a large deviation result for the posterior distribution (and, as a consequence, for Pitman estimators) in these models. A special attention is paid to weak convergence inside this class of models. In particular, we extend recent results by Dachian and Negri (2011) to a larger class of models.