No. 1090

Title:

Two sample test for diffusion processes with a non-linear covariate

Author(s):

Nishiyama, Yoichi (The Institute of Statistical Mathematics)

Key words:

Diffusion process, invariance principle, martingale, metric entropy, two sample test, weak convergence

Abstract:

    Let two diffusion processes $ t \leadsto X_t^{(p)} $, $ p=1,2 $, with the drift $ S^{(p)}(Z_t) $ where the covariate $ t \leadsto Z_t $ is common for $ p=1,2 $, be observed. We test whether the functions $ S^{(p)} $ for $ p=1,2 $ are the same or not. We present an asymptotically distribution free test and prove its consistency.