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Estimation de densité conditionnelle lorsque l'hypothèse de normalité est insatisfaisante

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  • Julie Carreau
  • Yoshua Bengio
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    Abstract

    We aim at modelling fat-tailed densities whose distributions are unknown but are potentially asymmetric. In this context, the standard normality assumption is not appropriate.In order to make as few distributional assumptions as possible, we use a non-parametric algorithm to model the center of the distribution. Density modelling becomes more difficult as we move further in the tail of the distribution since very few observations fall in the upper tail area. Hence we decide to use the generalized Pareto distribution (GPD) to model the tails of the distribution. The GPD can approximate finite, exponential or subexponential tails. The estimation of the parameters of the GPD is based solely on the extreme observations. An observation is defined as being extreme if it is greater than a given threshold. The main difficulty with GPD modelling is to determine an appropriate threshold. Nous cherchons à modéliser des densités dont la distribution est inconnue mais qui est asymétrique et présente des queues lourdes. Dans ce contexte, l'hypothèse de normalité n'est pas appropriée. Afin de maintenir au minimum le nombre d'hypothèses distributionnelles, nous utilisons une méthode non paramétrique pour modéliser le centre de la distribution. La modélisation est plus difficile dans les queues de la distribution puisque peu d'observations s'y trouvent. Nous nous proposons donc d'utiliser la Pareto généralisée (GPD) pour modéliser les queues de la distribution. La GPD permet d'approximer tous les types de queues de distributions (qu'elles soient finies, exponentielles ou sous-exponentielles). L'estimation des paramètres de la GPD est uniquement basée sur les observations extrêmes. Une observation est définie comme étant extrême si elle dépasse un seuil donné. La principale difficulté de la modélisation avec la GPD réside dans le choix d'un seuil adéquat.

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    Bibliographic Info

    Paper provided by CIRANO in its series CIRANO Working Papers with number 2004s-31.

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    Date of creation: 01 May 2004
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    Handle: RePEc:cir:cirwor:2004s-31

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    Related research

    Keywords: fat-tailed distribution; generalized Pareto; conditional density estimation; distribution à queue épaisse; Pareto généralisée; estimation de densité conditionnelle;

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    1. Phillipe Lambert & J. K. Lindsey, 1999. "Analysing Financial Returns by Using Regression Models Based on Non-Symmetric Stable Distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 409-424.
    2. Beirlant, Jan & Goegebeur, Yuri, 2003. "Regression with response distributions of Pareto-type," Computational Statistics & Data Analysis, Elsevier, vol. 42(4), pages 595-619, April.
    3. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
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