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On goodness-of-fit tests for parametric hypotheses in perturbed dynamical systems using a minimum distance estimator

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Abstract

We consider the problem of the construction of the goodness-of-fit test in the case of continuous time observations of a diffusion process with small noise. The null hypothesis is parametric and we use a minimum distance estimator of the unknown parameter. We propose an asymptotically distribution free test for this model.

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Acknowledgments

The author is grateful to Yu. A. Kutoyants for the statement of the problem and many helpful suggestions during the preparation of this paper. The author would like to thank the two Referees for the comments which allowed to improve essentially the exposition.

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  1. Laboratoire Manceau de Mathématiques, Université du Maine, 72085, Le Mans Cedex 9, France

    Maroua Ben Abdeddaiem

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  1. Maroua Ben Abdeddaiem
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Correspondence to Maroua Ben Abdeddaiem.

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Ben Abdeddaiem, M. On goodness-of-fit tests for parametric hypotheses in perturbed dynamical systems using a minimum distance estimator. Stat Inference Stoch Process 19, 259–287 (2016). https://doi.org/10.1007/s11203-016-9132-6

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  • DOI: https://doi.org/10.1007/s11203-016-9132-6

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