TY - JOUR

T1 - Goodness of fit test for small diffusions by discrete time observations

AU - Negri, Ilia

AU - Nishiyama, Yoichi

N1 - Funding Information:
Acknowledgments Part of this work was performed during the first author’s visit to Tokyo in December 2007 and the second author’s visit to Bergamo in May 2008 supported by MIUR 2006 Grant, and the kind hospitality of the Institute of Statistical Mathematics and the University of Bergamo is greatly appreciated. The authors thank Prof. Hiroki Masuda for helpful discussion, and the anonymous referee for constructive comments, especially for the suggestion on the estimator for ΣS0,σ as we stated in Sect. 5.

PY - 2011/4

Y1 - 2011/4

N2 - 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.

AB - 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.

KW - Asymptotically distribution free test

KW - Discrete time observations

KW - Small diffusion process

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U2 - 10.1007/s10463-009-0228-2

DO - 10.1007/s10463-009-0228-2

M3 - Article

AN - SCOPUS:79960096624

SN - 0020-3157

VL - 63

SP - 211

EP - 225

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

IS - 2

ER -