Parameter Resolution of the Estimation Methods for Power Law Indices

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.