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Entropy 2010, 12(6), 1581-1611; doi:10.3390/e12061581
Article

Projection Pursuit Through ϕ-Divergence Minimisation

Laboratoire de Statistique Théorique et Appliquée, Université Pierre et Marie Curie, 175 rue du Chevaleret, 75013 Paris, France
Received: 8 April 2010 / Revised: 27 May 2010 / Accepted: 31 May 2010 / Published: 14 June 2010
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Abstract

In his 1985 article (“Projection pursuit”), Huber demonstrates the interest of his method to estimate a density from a data set in a simple given case. He considers the factorization of density through a Gaussian component and some residual density. Huber’s work is based on maximizing Kullback–Leibler divergence. Our proposal leads to a new algorithm. 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.
Keywords: projection pursuit; minimum ϕ-divergence; elliptical distribution; goodness-of-fit; copula; regression projection pursuit; minimum ϕ-divergence; elliptical distribution; goodness-of-fit; copula; regression
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Touboul, J. Projection Pursuit Through ϕ-Divergence Minimisation. Entropy 2010, 12, 1581-1611.

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