联合均值和散度逆高斯回归模型的参数估计

Parameter Estimation of Joint Mean and Inverse Gaussian Regression Model of Dispersion

逆高斯回归模型可用于分析正偏态数据,人们通常研究解释变量对其均值参数的影响,但往往忽略了对其散度参数的影响,文章则基于解释变量对均值和散度都有影响的前提,针对联合均值和散度逆高斯回归模型,探讨模型参数的极大似然估计问题。MM算法在优化问题上具有分离参数、降低目标函数的维度、简化求解过程等优点,将MM算法应用于联合均值和散度逆高斯回归模型,能将多元似然函数彻底分解为一系列一元函数之和,从而绕开了参数估计中的矩阵求逆问题。模拟研究表明,当数据量达到100时就能得到很好的估计效果;实证分析表明,理论研究在实际应用中具有可行性。

Inverse Gaussian regression models can be used to analyze positive skewness data.People usually study the influence of explanatory variables on their mean parameters,but often ignore the influence on their dispersion parameters.Based on the premise that explanatory variables have an effect on both mean and dispersion,this paper discusses the maximum likelihood estimation of model parameters for the joint mean and inverse Gaussian regression model of dispersion.In terms of optimization,MM algorithm has the advantages of separating parameters,reducing the dimension of objective function,simplifying the solving process and so on.MM algorithm applied to joint mean and the inverse Gaussian regression model of dispersion,the multivariate likelihood function can be completely decomposed into the sum of a series of unary functions,thus bypassing matrix inversion in parameter estimation.Simulation studies show that good estimation effect can be obtained when the amount of data reaches 100.The empirical analysis shows that the theoretical research is feasible in practical application.