No. 1095

Title:

Two sample test for counting processes with a non-linear covariate based on smoothed empirical processes

Author(s):

Nishiyama, Yoichi (The Institute of Statistical Mathematics)

Key words:

Counting process, invariance principle, martingale, two sample test, weak convergence.

Abstract:

    We consider a non-linear model $ \alpha(Z_{t}) $ of the intensity of counting processes $ N $ with a real-valued covariate $ Z $, where $ \alpha(\cdot) $ is a deterministic function. Given two processes $ N^{(p)} $, we test whether the functions $ \alpha^{(p)} $ for $ p=1,2 $ are the same or not, where the covariate $ Z $ is common for $ p=1,2 $. We present an asymptotically distribution free test and prove its consistency.