On the goodness-of-fit testing for ergodic diffusion processes
Yury A. Kutoyants · Journal of nonparametric statistics · 2009
We consider the goodness-of-fit testing problem for ergodic diffusion processes. The basic hypothesis is supposed to be simple. The diffusion coefficient is known and the alternatives are described by the different trend coefficients. We study the asymptotic distribution of the Cramér–von Mises type tests based on the empirical distribution function and local time estimator of the invariant density. Particularly, we propose a transformation which makes these tests asymptotically distribution-free.