Goodness of fit test for small diffusions by discrete time observations

Ilia Negri, Yoichi Nishiyama*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)211-225
Number of pages15
JournalAnnals of the Institute of Statistical Mathematics
Issue number2
Publication statusPublished - 2011 Apr
Externally publishedYes


  • Asymptotically distribution free test
  • Discrete time observations
  • Small diffusion process

ASJC Scopus subject areas

  • Statistics and Probability


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