论文标题
一种预期最大化算法，用于估计相关二项式分布的参数
An expectation-maximization algorithm for estimating the parameters of the correlated binomial distribution
论文作者
论文摘要
相关的二项式（CB）分布是由Luceño（计算统计$ \＆$数据分析，20，1995，511-520）提出的，作为二项式分布的替代方案，用于在事件之间存在相关性的情况下分析数据。由于模型的混合物可能性的复杂性，可能无法得出未知参数的最大似然估计器（MLE）的分析表达式。为了克服这一困难，我们开发了一种用于计算CB参数MLE的期望最大化算法。模拟研究和真实数据应用的数值结果表明，该方法通过始终达到全局最大值非常有效。最后，我们的结果应该引起高级本科生或一年级研究生及其讲师的关注，重点是EM算法在离散混合模型中查找参数MLE的感兴趣应用。
The correlated binomial (CB) distribution was proposed by Luceño (Computational Statistics $\&$ Data Analysis, 20, 1995, 511-520) as an alternative to the binomial distribution for the analysis of the data in the presence of correlations among events. Due to the complexity of the mixture likelihood of the model, it may be impossible to derive analytical expressions of the maximum likelihood estimators (MLEs) of the unknown parameters. To overcome this difficulty, we develop an expectation-maximization algorithm for computing the MLEs of the CB parameters. Numerical results from simulation studies and a real-data application showed that the proposed method is very effective by consistently reaching a global maximum. Finally, our results should be of interest to senior undergraduate or first-year graduate students and their lecturers with an emphasis on the interested applications of the EM algorithm for finding the MLEs of the parameters in discrete mixture models.
