通过$Φ$的投影寻踪-发散最小化
Projection Pursuit through $Φ$-Divergence Minimisation
摘要：
考虑在一个非常大的维度集合上定义的密度。很难从一组数据中估计出这个密度。然而，它是可能的，通过投影寻踪方法来解决这个问题。Touboul的文章“通过相对熵最小化的投影寻踪”，2009年，展示了作者的方法在一个非常简单的给定情况下的兴趣。他认为通过一个椭圆分量和一些剩余密度的因式分解。上述Touboul的工作是基于最小化相对熵。在本文中，我们的建议旨在将这种方法扩展到$Φ-$分歧。此外，我们还将考虑要因子分解的密度是从i.i.d.估计的情况。sample.然后，我们将提出一个测试的估计密度的因式分解。应用程序包括一个新的测试适合有关的椭圆copula。
英文摘要：
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 Touboul'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.
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