No. 1116

Title:

A martigale central limit theorem in Hilbert space and its applications

Author(s):

Nishiyama, Yoichi (The Institute of Statistical Mathematics)

Key words:

Martingale, weak convergence in Hilbert space, goodness-of-fit test, Cram\'er-von Mises test.

Abstract:

    The first goal of this paper is to establish a central limit theorem for the sum of Hilbert space valued random elements in terms of martingale type conditions. As its applications, we consider two kinds of goodness-of-fit test problems for ergodic diffusion processes based on discrete observations. We propose Cram\'er-von Mises type tests, and prove that they are asymptotically distribution free under a simple null hypothesis and that they are consistent under any fixed alternatives.