有限样本分形维数估计的研究

Research on the Estimation of Fractal Dimension under Finite Sample

分形维数的正确估计是非常重要的。通过对一种计盒维数估计方法的研究，推导出了有限样本条件下，计盒维数估计的理论尺度下界，提出了一种有限样本条件下提高分形维数估计准确性的递归优化算法。

The accurate estimation of fractal dimension is very important. In this paper a kind of box counting method named reticular cell counting is analyzed and the lower bound for theoretical box size under finite sample is deduced. Furthermore an iterative and optimal algorithm for the accurate estimation of fractal dimension is proposed and the analysis for applications is given.