NONPARAMETRIC ESTIMATION AND TESTING TIME HOMOGENITY FOR LEVY PROCESS

Yoichi NISHIYAMA

The Institute of Statistical Mathematics, Tokyo
Japan

ABSTRACT

We consider a nonparametric estimation problem of the Lévy measure of time-inhomogeneous Léevy process. We derive thef 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.

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