A Consistent Approach to Least Squares Estimation of Correlation Dimension in Weak Bernoulli Dynamical Systems

Abstract

A new approach to the least squares procedure for correlation dimension estimation is suggested. Consistency of the new estimator is established for a class of dynamical systems that includes the Cantor map and the logistic map with parameter value 4. Unlike the proofs of consistency for other estimation procedures, no assumptions are made about the Grassberger-Procaccia spatial correlation integral beyond the existence of the correlation dimension.