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分形维数盒计数估计量的表现AI 解读

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…

条件分布的Bootstrap估计AI 解读

Techniques are developed for bootstrap estimation of conditional distributions, with application to confidence intervals and hypothesis tests for one parameter, conditional on the value of an estimator of another. Both Monte Carlo and saddlepoint methods for approximating bootstrap distributions are considered, and empirical methods are suggested for implementing these techniques. For example, in the case of Monte Carlo methods, we suggest empirical techniques for selecting…