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Analyse comparative des tests de permutations en régression multiple et application à l'analyse de tableaux de distances.

Abstract : When the data generation process does not satisfy some of the assumptions founding the statistical inferences in the classic linear regression model, permutation tests offer a reliable nonparametric alternative for constructing distribution-free tests. The first application of the permutation test methodology for statistical inference on the simple linear regression model can be traced back to papers by Fisher (1935) and Pitman (1937a, b, 1938). This resampling method is founded on hypothesis weaker than the classic parametric approach and which are easily checkable in practice: the exchangeability of the observations under the null hypothesis. There is general agreement concerning an appropriate permutation method yielding exact tests of hypotheses in the simple linear regression model. This is not the case, however, for partial tests needed in multiple linear regressions. Then, the problem becomes much trickier to test a null hypothesis concerning one partial regression coefficient. Due exchangeability properties are no more satisfied, and thus no exact test exists for that problem. Several asymptotically exact candidate methods have been proposed in that case.
The main goal of our work aims at comparison of permutation test startegies adapted to the hypotheses of nullity of a partial coefficient regression in a linear regression model with p explanatory variables, conditionally on the information contained in the sample at hand. Four permutation test methods are compared, first on simulated data resorting to the double linear regression model, and then on theoretical grounds, in order to explore their unbiasedness properties, as well as their power function's hierarchy. The results obtained are then extended to the general multiple linear regressions setting.
A final chapter supplements our research by focussing on inferential problems met when dealing with partial dependence structures between inter-point distance matrices of finite order. We compared the adaptation of four candidate permutation test strategies in this context, the specificity of which relies on the complexities induced by the dependence structure existing between elements of a distance matrix. Therefore, we obtained results that revealed themselves quite different in this case from those obtained in the classic situation of linear regression applied to independent samples, which is the object of our simulations and formal developments presented in the first part of the thesis.
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https://tel.archives-ouvertes.fr/tel-00201481
Contributor : Ali Shadrokh <>
Submitted on : Sunday, December 30, 2007 - 6:37:27 AM
Last modification on : Friday, November 6, 2020 - 4:44:45 AM
Long-term archiving on: : Tuesday, April 13, 2010 - 3:11:24 PM

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Ali Shadrokh. Analyse comparative des tests de permutations en régression multiple et application à l'analyse de tableaux de distances.. Mathématiques [math]. Université Joseph-Fourier - Grenoble I; Université Pierre Mendès-France - Grenoble II, 2007. Français. ⟨tel-00201481⟩

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