This paper considers the problem of robustly estimating the parameters of a heavy-tailed multivariate distribution when the covariance matrix is known to have the structure of a low-rank matrix plus a diagonal matrix as considered in factor analysis (FA). By assuming the observed data to follow the multivariate Student's t distribution, we can robustly estimate the parameters via maximum likelihood estimation (MLE). However, the MLE of parameters becomes an intractable problem when the multivariate Student's t distribution and the FA structure are both introduced. In this paper, we propose an algorithm based on the generalized expectation maximization (GEM) method to obtain estimators. The robustness of our proposed method is further enhanced to cope with missing values. Finally, we show the performance of our proposed algorithm using both synthetic data and real financial data.

翻译：本文考虑了当共变矩阵已知具有系数分析(FA)中考虑的低级矩阵结构加上对等矩阵时,对重尾多变量分布参数进行严格估算的问题。假设观察到的数据遵循多变量学生 t分布,我们可以通过最大可能性估计(MLE)对参数进行严格估算。然而,当引入多变量学生 t分布法和FA结构时,参数的 MLE就成为一个棘手的问题。在本文中,我们根据普遍预期最大化(GEM)方法提出一种算法,以获取估计数据。我们拟议方法的稳健性得到进一步提高,以适应缺失的价值。最后,我们用合成数据和实际财务数据来显示我们提议的算法的性能。