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

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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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) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Touboul, J. Projection Pursuit Through ϕ-Divergence Minimisation. Entropy 2010, 12, 1581-1611.

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