J. Japan Statist. Soc., Vol. 35 (No. 2), pp. 287-302, 2005

Estimating the correlation dimension from a chaotic system with dynamic noise

Atsushi Kawaguchi, Koji Yonemoto and Takashi Yanagawa

Abstract. This paper proposes an estimator of the correlation dimension of the skeleton for chaotic dynamical system with dynamic noise and prove the consistency of the estimator under some assumptions.

Key words and phrases: Chaotic dynamical system, correlation dimension, \break Nadaraya-Watson kernel type estimator, U-statistics.