Goodness of fit test for small diffusions by discrete observations

2008/01/27 by Ilia Negri, Negri, Ilia, Yoichi Nishiyama +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Statistics Theory (math.ST) #advanced mathematical theories #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.0801.4146

arxiv created 2008/01/27 · openalex publication_date 2008/01/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Citations

• Foundations of Modern Probability

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