An improved estimator of dimension and some comments on providing confidence intervals

An estimator of dimension is described that has many advantages over the conventional implementation of the Grassberger-Procaccia method. It can in some circumstances provide a confidence interval for the dimension estimate. For high dimension sets (greater than about 3.5) the dimension estimate has a bias which depends on the structure of the set. If one has suitable knowledge of the structure of the set it is possible to make a bias adjustment. Some numerical calculations are presented which indicate the largest error in the dimension estimate that can be expected. The problem of providing confidence intervals for dimension estimates in general is not solved completely, but we do take a step away from a meaningless number.