On the Performance of Box-Counting Estimators of Fractal Dimension
研究了盒计数估计量在估计分形维数时的随机性质，推导了高斯过程模型下估计量的渐近偏差和方差公式，并比较了两种不同形式的估计量。
Box-counting estimators are popular for estimating fractal dimension. However, very little is known of their stochastic properties, despite increasing statistical interest in their application. We show that, if the irregular curve to which the estimators are applied is modelled by a Gaussian process, concise formulae may be developed for asymptotic bias and variance of box-counting estimators. These formulae point to critical differences between a native form of the box-counting estimator, based directly on the capacity definition of fractal dimension, and a regression-inspired version of that estimator.