Projection Pursuit Through Relative Entropy Minimization

Projection Pursuit methodology permits to solve the difficult problem of finding an estimate of a density defined on a set of very large dimension. In his seminal article, "Projection Pursuit", Huber (1985) evidenced the interest of the Projection Pursuit method thanks to the factorization of a density into a Gaussian component and some residual density in a context of Kullback-Leibler divergence maximisation. In the present article, we introduce a new algorithm, and in particular, a test for the factorisation of a density estimated from an iid sample.