In the context of model selection by minimization of penalized contrast, since the original work of Akaike in 1974 followed later in 1999 by the work of Barron, Birgé and Massart (1999), a question remains : how to build a data-driven penalized procedure which offers both good theoretical quality and good empirical behavior ?

Since Comte and Rozenholc (2002, 2004) where already a plug-in approach was proposed to answer this question, several attempts have been proposed in the more recent years and we can cite two main approaches : "dimension jump" and "slope heuristic", referring non exhaustively to Birgé and Massart (2006), Lebarbier (2005), Arlot and Massart (2009), Baudry et al. (2008), Baudry et al. (2012) but also Baraud, Giraud and Huet (2009). Unfortunately such approaches offer unstable solutions which need to be stabilized in order to be used from a practical point of view and/or which are not easily implementable.

In this talk, I will present in the fixed design homoscedastic regression setting a new fully data-driven procedure for model selection called "Statistical Base Jumping" which offers the benefit to be both stable and easily implementable. Several heuristics justifying this construction will be provided and simulations will show that its is safely controlled in term of risk. Finally, I will show how this construction can be extended to other models.