Projection Pursuit Through Relative Entropy Minimization

Abstract

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.

Keywords:

• Elliptical distribution
• Minimum Kullback–Leibler divergence maximization
• Projection pursuit
• Robustness

Mathematics Subject Classification:

• 62H40
• 62G07
• 62G20
• 62H11

Notes

Therefore, we conclude that f = g ⁽²⁾.

Therefore, we conclude that f = g ⁽¹⁾.

Therefore, we conclude that f = g ⁽¹⁾.