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Test d'ajustement d'un processus de diffusion ergodique à changement de régime

Abstract : We consider the Cramér-von Mises goodness-of-fit type tests to test the hypothesis that the observed diffusion process is "switching diffusion", i.e., this process has sign-type trend coefficient. These tests are based on empirical distribution and empirical density functions. It is shown that the limit distributions of the proposed test statistics are defined by the integral type functionals of continuous Gaussian processes. We provide the Karhunen-Loéve expansion of the corresponding limiting processes. This expansion allows us to simplify the problem of the calculation of the thresholds. We study the behavior of these statistics under alternatives and we show that these tests are consistent. To treat the composite basic hypotheses we need to know the asymptotic behavior of statistical estimators of the unknown parameters. That is why we consider the problem of parameter estimation for switching diffusion process. We suppose that the unknown parameter is two-dimensional and we describe the asymptotic properties of the maximum likelihood and Bayesian estimators in this case. Using these estimators we construct the corresponding Cramér-von Mises type tests and study their limit distributions. Finally we consider two Cramér-von Mises type tests for ergodic diffusion process in the general case. It is shown that for a certain choice of weight functions these tests are asymptotically distribution-free. For some particular cases, we provide the explicit expressions of the limit distributions of these statistics via direct calculation of Laplace transforms.
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https://tel.archives-ouvertes.fr/tel-00543318
Contributor : Anis Gassem <>
Submitted on : Monday, December 6, 2010 - 1:15:43 PM
Last modification on : Tuesday, March 31, 2020 - 3:21:49 PM
Long-term archiving on: : Monday, March 7, 2011 - 3:19:46 AM

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  • HAL Id : tel-00543318, version 1

Citation

Anis Gassem. Test d'ajustement d'un processus de diffusion ergodique à changement de régime. Mathématiques [math]. Université du Maine, 2010. Français. ⟨tel-00543318⟩

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