不同类型数据下混合模型参数估计效果的对比研究

Comparative Study on Effects of Parameter Estimation of Mixture Models under Different Types of Data

摘要: 混合高斯模型在描述数据方面应用较多，但它易受离群点的影响，其参数的极大似然估计不是稳健估计。混合t-分布模型由于其重尾分布的特性，相对于混合高斯分布，在分析重尾数据上更具稳健性。文章首先研究一元混合t-分布模型，利用标准EM算法给出了该模型参数极大似然估计的迭代步骤，并分别在三类模拟数据下与混合高斯模型进行了对比分析，验证了该模型的有效性以及在拟合重尾数据上的优势。算法初始化采用k-means方法。

Abstract: The normal mixture model has more applications in describing data. But it is easily influenced by the outlier, and the maximum likelihood estimation of parameters is not robust estimation. T-distribution mixture model has better robustness than Gauss mixture model to analyze data with longer time than normal tails because of its heavy-tails. In this paper, we studied a univariate t mixture model primarily. Based on EM algorithm, we derived the iteration steps of maximum li-kelihood estimation of the model’s unknown parameters. Furthermore, we did a comparative analysis by three types of simulated data. Simulation study shows that this model has an advantage in fitting data with longer time than normal tails. The initial value is given by k-means method.