Goodness of fit test for small diffusions by discrete observations

Details Goodness of fit test for small diffusions by discrete observations Goodness of fit test for small diffusions by discrete observations

2008-01-27

arxiv.org/abs/0801.4146v1

Mathematics

Statistics Theory

Scientific paper

We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional small diffusions. Our test is based on discrete observation of the processes, and the diffusion coefficient is a nuisance function which is estimated 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 alternatives.

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