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Contributions à la prévision statistique

Abstract : In a first part, the aim is to predict, in the sense of forecasting, a future value of a stochastic process, whose law is indexed by an unknown parameter, from observing its past trajectory. More precisely, it is shown on an additive regression model, how one can separate, by a time-splitting device, the statistical estimation problem from the probabilistic calculus of the predictor. The asymptotic convergence properties of the obtained genuine statistical predictor are studied.
In a second part, the aim is to predict, in the sense of explaining, a random variable Y by a another r.v. X. To that purpose, the goal is to estimate the conditional density of Y given X=x from an iid sample. A new product shaped estimator is proposed, based on the quantile transform and the copula representation, whose asymptotic convergence properties are studied. We show how it can compare favourably to its ratio-shaped competitors, and propose several variants and extensions. At last, the properties of the predictors associated to this estimator such as the regression function, the conditional mode and the highest density regions are studied. Some applications, connections and perspectives are also sketched.
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https://tel.archives-ouvertes.fr/tel-00370418
Contributor : Olivier P. Faugeras <>
Submitted on : Tuesday, March 24, 2009 - 1:14:00 PM
Last modification on : Wednesday, December 9, 2020 - 3:14:34 PM
Long-term archiving on: : Friday, October 12, 2012 - 2:15:43 PM

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  • HAL Id : tel-00370418, version 1

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Olivier P. Faugeras. Contributions à la prévision statistique. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2008. Français. ⟨tel-00370418⟩

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