Projection Pursuit Through Relative Entropy Minimization

Consider a de ned density on a set of very large dimension. It is quite di cult to nd an estimate of this density from a data set. However, it is possible through a projection pursuit methodology to solve this problem. In his seminal article, Huber (see "Projection pursuit", Annals of Statistics, 1985) demonstrates the interest of his method in a very simple given case. He considers the factorization of density through a Gaussian component and some residual density. Huber's work is based on maximizing relative entropy. Our proposal leads to a new algorithm. Furthermore, we consider the case when the density to be factorized is estimated from an i.i.d. sample. In this case, we will propose a test for the factorization of the estimated density.