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.
- Asymptotically distribution-free test
- Discrete-time observation
- Ergodic diffusion process
- Invariance principle
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty