Comparison Between the Two Models: New Approach Using the α−Divergence

We propose new nonparametric accordance Rényi-α and α-Tsallis divergence es-timators for continuous distributions. We discuss this approach with a view to the selection model (on altoire and autoregressive AR (1)). We lestimateur used by kernel density esttimer underlying. Nevertheless, we are able to prove that the esti-mators are consistent under certain conditions. We also describe how to apply these estimators and demonstrate their effectiveness through numerical experiments. Key words: test de racine unitaire, modéle AR(1), α−Divergence. AMS Subject Classification: 60J60, 62F03, 62F05, 94A17.