Comparaison between the two models : new approach using the $\alpha$-divergence

Abstract

We propose new nonparametric accordance R\'enyi-$\alpha$ and $\alpha$-Tsallis divergence estimators for continuous distributions. We discuss this approach with a view to the selection model (on al\'etoire and autoregressive AR (1)). We lestimateur used by kernel density esttimer underlying. Nevertheless, we are able to prove that the estimators are consistent under certain conditions. We also describe how to apply these estimators and demonstrate their effectiveness through numerical experiments.