Projection Pursuit Through ϕ-Divergence Minimisation

Jacques Touboul
2010 Entropy  
Consider a defined density on a set of very large dimension. It is quite difficult to find an estimate of this density from a data set. However, it is possible through a projection pursuit methodology to solve this problem. Touboul's article "Projection Pursuit Through Relative Entropy Minimization", 2009, demonstrates the interest of the author's method in a very simple given case. He considers the factorization of a density through an Elliptical component and some residual density. The above
more » ... ouboul's work is based on minimizing relative entropy. In the present article, our proposal will aim at extending this very methodology to the Φ-divergence. Furthermore, we will also consider the case when the density to be factorized is estimated from an i.i.d. sample. We will then propose a test for the factorization of the estimated density. Applications include a new test of fit pertaining to the Elliptical copulas.
doi:10.3390/e12061581 fatcat:s6ussohvs5fyhftbw2maj6edfq