Goodness-of-fit test for ergodic diffusions by discrete-time observations: An innovation martingale approach

Hiroki Masuda, Ilia Negri, Yoichi Nishiyama

Research output: Contribution to journalArticle

5 Citations (Scopus)


We consider a nonparametric goodness-of-fit test problem for the drift coefficient of one-dimensional ergodic diffusions. Our test is based on the 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 alternatives.

Original languageEnglish
Pages (from-to)237-254
Number of pages18
JournalJournal of Nonparametric Statistics
Issue number2
Publication statusPublished - 2011 Jun 1



  • Asymptotically distribution-free test
  • Discrete-time observation
  • Ergodic diffusion process
  • Invariance principle

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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