No. 1094

Title:

Nonparametric goodness of fit tests for ergodic diffusion processes by discrete observations

Author(s):

Nishiyama, Yoichi (The Institute of Statistical Mathematics)

Key words:

Asymptotically distribution free test, discrete observation, invariance principle, goodness of fit test.

Abstract:

    This paper considers two kinds of goodness of fit test problems for the drift coefficeint $ S $ and the diffusion coefficient $ \sigma^2 $ of ergodic diffusion processes based on discrete observations. One is testing the hypothesis $ H_0: S=S_{0} $ for a given $ S_{0} $ with $ \sigma $ being an unknown nuisance function, while the other is tesing the hypothesis $ H_{0}: \sigma=\sigma_{0} $ for a given $ \sigma_{0} $ with $ S $ being an unknown nuisance function. For both problems we propose some asymptotically distribution free tests, and prove their consistency under any fixed alternatives.