Abstract
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.
Highlights
Discrete Dynamics in Nature and Society different
In order to study the relationships between the parameter resolution and the influencing factors, this paper selects different discrimination methods, estimation algorithms, parameter values, and noise types. e research shows that the classification algorithm has lower error rate, and lsqcurvefit algorithm can distinguish two more similar signals; with the increase of parameter values, the accuracy of parameter resolution is lower
The similar signals are more difficult to be separated, and the absolute error of local parameters is small; it is found that when the parameter estimation is asymptotically normal, the parameter resolution can be predicted by interval estimation, and other cases can be obtained by experimental calculation; the accuracy of parameter resolution increases with the increase of signal-to-noise ratio and decreases with the increase of noise intensity
Summary
Discrete Dynamics in Nature and Society different. the selection of the model and algorithm is important in the data analysis. e model and algorithm can be evaluated from the following four aspects: accuracy, robustness, calculation speed, and simplicity of the model. Is paper puts forward the concept of parameter resolution, which is used to evaluate the accuracy of model and algorithm. The power-law model is selected, and the parameter resolution is studied by using nonlinear leastsquare method and maximum likelihood method. In order to study the relationships between the parameter resolution and the influencing factors, this paper selects different discrimination methods, estimation algorithms, parameter values, and noise types. E research shows that the classification algorithm has lower error rate, and lsqcurvefit algorithm can distinguish two more similar signals; with the increase of parameter values, the accuracy of parameter resolution is lower. The parameter resolution of an algorithm depends on model, noise, and sample size as well as the criterion to distinguish two close signals.
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