No. 997

Title:

Nonparametric estimation and testing time-homogeneity for Lévy processes

Author(s):

Nishiyama, Yoichi (The Institute of Statistical Mathematics)

Key words:

Empirical process, Levy process, martingale, nonparametric estimation, change point problem.

Abstract:

    We consider a nonparametric estimation problem of the Lévy measure of time-inhomogeneous Lévy process. We derive the functional asymptotic normality and efficiency, in an $ \ell ^\infty $-space, of generalized Nelson-Aalen estimators. Also we propose some asymptotically distribution free tests for time-homogeneity of the Lévy measure. Our result is a fruit of the empirical process theory and the martingale theory.