峰度与偏度系数的近似经验贝叶斯估计

The Approximate Empirical Bayesian Estimation of Kurtosis and Skewness Coefficient

建立了单样本数据的贝叶斯模型,给出了偏度系数和峰度系数的线性贝叶斯估计及近似信度估计.进而,将模型推广到多样本数据模型下,并讨论了近似信度估计的统计性质,比较了贝叶斯估计、线性贝叶斯估计及近似信度估计的均方误差.最后,给出了超参数的估计,得到了近似信度估计的经验贝叶斯估计,使该估计可直接运用于实际问题.

A Bayesian model of single sample data is established,and the Bayesian estimation,linear Bayesian estimation and approximate credibility estimation of skewness and kurtosis coefficient are given. Furthermore,the model is extended to multitude data model. In this model,the statistical properties of approximate credibility estimation are discussed,the mean square errors of Bayesian estimation,linear approximation and approximate credibility estimation are compared. Finally,the estimation of supper-parameters are given,thus the empirical Bayes estimation of approximate credibility estimation is derived,and it can be directly applied to practice.