Statistical Error in Dimension Estimators
The statistical error in an estimate of the correlation dimension based on a sample of N points (e.g., from a time series) generically scales as O(\(1/\sqrt N \)). The coefficient of the \(1/\sqrt N \) term can be related to the variance over the attractor of the pointwise mass function. In many cases, the coefficient is small, and for very particular examples the coefficient is zero. In the latter case, anomalously precise O(1/N) scaling is obtained. These results are shown to have practical implications for computing the dimension of an attractor from a time series.
KeywordsStatistical Error Correlation Dimension Dimension Estimate Strange Attractor Statistical Precision
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