The accuracy of parameter estimation plays an important role in economic and social models and experiments. Parameter resolution is the capability of an estimation algorithm to distinguish different parameters effectively under given noise level, which can be used to select appropriate algorithm for experimental or empirical data. We use a flexible distinguishing criterion and present a framework to compute the parameter resolution by bootstrap and simulation, which can be used in different models and algorithms, even for non-Gaussian noises. The parameter resolutions are computed for power law models and corresponding algorithms. For power law signal, with the increase of SNR, parameter resolution is finer; with the decrease of parameter, the resolution is finer. The standard deviation of noise and parameter resolution satisfies the linear relation; it relates to interval estimation naturally if the estimation algorithm is asymptotically normal. For power law distribution, parameter and resolution satisfy the linear relation, and experimental slope and theoretical slope tend to be consistent when significance level approaches zero. Last, we select an algorithm with finer resolution to estimate the Pareto index for the Forbes list of global rich data in recent 10 years and analyze the changes in the gap between the rich and the poor.

中文翻译：

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幂律指数估计方法的参数解析

参数估计的准确性在经济和社会模型和实验中起着重要作用。参数分辨率是估计算法在给定噪声水平下有效区分不同参数的能力，可用于为实验或经验数据选择合适的算法。我们使用灵活的区分标准并提出了一个框架来通过引导和模拟计算参数分辨率，该框架可用于不同的模型和算法，甚至可以用于非高斯噪声。计算幂律模型和相应算法的参数分辨率。对于幂律信号，随着信噪比的增加，参数分辨率更精细；参数越小，分辨率越细。噪声与参数分辨率的标准偏差满足线性关系；如果估计算法是渐近正态的，它自然与区间估计有关。对于幂律分布，参数和分辨率满足线性关系，当显着性水平接近于零时，实验斜率和理论斜率趋于一致。最后，我们选择分辨率更精细的算法对福布斯近10年全球富豪数据排行榜进行帕累托指数估计，分析贫富差距的变化。当显着性水平接近零时，实验斜率和理论斜率趋于一致。最后，我们选择分辨率更精细的算法对福布斯近10年全球富豪数据榜单进行帕累托指数估计，分析贫富差距的变化。当显着性水平接近零时，实验斜率和理论斜率趋于一致。最后，我们选择分辨率更精细的算法对福布斯近10年全球富豪数据榜单进行帕累托指数估计，分析贫富差距的变化。