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Goodness of fit test for small diffusions by discrete time observations

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Abstract

We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional small diffusions. Our test is based on discrete time observation of the processes, and the diffusion coefficient is a nuisance function which is “estimated” in some sense in our testing procedure. We prove that the limit distribution of our test is the supremum of the standard Brownian motion, and thus our test is asymptotically distribution free. We also show that our test is consistent under any fixed alternative.

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Authors and Affiliations

  1. University of Bergamo, Viale Marconi 5, 24044, Dalmine, BG, Italy

    Ilia Negri

  2. The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo, 106-8569, Japan

    Yoichi Nishiyama

Authors
  1. Ilia Negri
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  2. Yoichi Nishiyama
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Correspondence to Yoichi Nishiyama.

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Negri, I., Nishiyama, Y. Goodness of fit test for small diffusions by discrete time observations. Ann Inst Stat Math 63, 211–225 (2011). https://doi.org/10.1007/s10463-009-0228-2

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  • DOI: https://doi.org/10.1007/s10463-009-0228-2

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