  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.
