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Simulations using ``ideal data''

From one thousand Monte Carlo trials of the dimension and entropy estimates using simulated data, i.e. independent distances drawn from the distribution (equation (3)), the means and variances were estimated. These were compared with the specified $\nu$ and $K_2$ and the asymptotic variances. The estimators and the expressions for the asymptotic variances appear to be accurate if both $N_{l,d}+N_{s,d}$ and $N_{l,d+e}+N_{s,d+e}$ are larger than about 50.