Title: About the correction term in a small--ball probability factorization
Authors: Enea Bongiorno - Universita del Piemonte Orientale (Italy) [presenting]
Aldo Goia - University of Eastern Piedmont Amedeo Avogadro (Italy)
Philippe Vieu - University Paul Sabatier (France)
Abstract: A d-dimensional factorization of the small ball probability is considered: it involves three terms that play the roles of a surrogate density, a volumetric term and a correction factor. The latter factor is studied, and it is shown how it can be used to locally identify the dimension of curves. To make operative the dimension detector, an empirical estimator of the correction factor is introduced, and some asymptotics are presented. Some simulations show the potentiality of this new tool.