广义t分布的EM估计

EM estimation of generalized t distributions

在广义t分布的自由度参数未知时,自由度参数的最大似然估计不存在,而矩估计和最大似然估计不相合。通过建立广义t分布和正态混合分布之间的关系,能够在不完全数据框架下讨论自由度参数的最大似然估计。给出了广义t分布的Bayes分层表达,证明了参数的共轭先验和两类隐变量的数学期望。讨论并分析了广义t分布的EM类算法及估计的标准差的计算。通过Monte Carlo模拟,分析了广义t分布的参数估计问题。

Under the assumption that the degree of freedom parameter （df） of the generalized t distributions is unknown, the maximum likelihood estimator （MLE） of df does not exist, the moment estimator is inconsistent with MLE. The generalized t distributions are an infinite mixture of Normal distribution from incomplete data perspectives. The hierarchical bayesian models of the generalized t distributions were discussed, and the expectations of two latent variables were obtained. The EM-type algorithm of the generalized t distributions were discussed on the estimated standard errors, a simulation study was conducted to assess the performanee of proposed methods. Simulation results confirm the problems of the degree of freedom parameter in the case of small samples and larger samples.