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Un test d'adéquation global pour la fonction de répartition conditionnelle

Abstract : Let (X;Y) be a random real vector. Many statistical procedures allow to fit models to such data but this usually requires many assumptions that must somehow be validated before the model can be used with some degree of confidence. In this work, we propose a global test that can assess the validity of the supposed model by testing simultaneously all the hypotheses made about the model. This test is based on a quantity that embodies all the information about the joint behaviour of X and Y : the conditional distribution function F(y|x)=P(Y<=y|X=x) and on a standard paradigm that consists in comparing the local polynomial estimator of F(y|x) with a parametric one and rejecting the model if the distance between these two quantities exceeds a critical value. In the first part, we give the asymptotic behaviour of our test statistic when the supposed conditional distribution function does not involve unknown parameters. In a second part, we generalize to the case where such parameters are involved. Then, we give the local asymptotic power of the test by studying its asymptotic behaviour under contiguous alternatives. Finally, we propose a choice for the bandwidth parameter used in the local polynomial estimation of
the distribution function.
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https://tel.archives-ouvertes.fr/tel-00008559
Contributor : Sandie Ferrigno <>
Submitted on : Wednesday, February 23, 2005 - 5:00:43 PM
Last modification on : Wednesday, October 11, 2017 - 1:12:38 AM
Long-term archiving on: : Friday, April 2, 2010 - 9:31:53 PM

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  • HAL Id : tel-00008559, version 1

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Sandie Ferrigno. Un test d'adéquation global pour la fonction de répartition conditionnelle. Mathématiques [math]. Université Montpellier II - Sciences et Techniques du Languedoc, 2004. Français. ⟨tel-00008559⟩

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