联合均值与方差混合专家回归模型的参数估计

在社会、经济领域中存在大量来自异质总体的异方差数据.本文针对异质总体的异方差数据,研究提出联合均值与方差混合专家回归模型,该模型同时对感兴趣的均值、方差和混合比例参数建模,可以概括和描述众多的实际问题.然后,利用EM算法和MM算法给出该模型的最大似然估计,进而通过Monte Carlo随机模拟来验证所提出的方法的有效性.最后,本文结合实际数据AQI(空气质量指数)说明模型的实用性和可行性.

The Parameter Estimation of the Mixture of Experts Regression for Joint Mean and Variance Models

In social and economic fields, there are lots of heteroscedastic data from heterogeneous population. To the heteroscedastic data of heterogeneous populations, we propose mixture expert regression for joint mean and variance models, which is used to simultaneously model the mean, variance and mix proportion parameters of interest. Many practical problems can be described and summarized by this model. EM and MM algorithm is considered to estimate unknown parameters in the maximum likelihood estimation procedure. Monte Carlo simulation is used to verify the proposed method. Finally, combining with the actual data of AQI(Air Quality Index) shows the feasibility and practicability of the models.