Robust Factor Analysis Parameter Estimation

TL;DR

This paper introduces a robust parameter estimation method for factor analysis models with heavy-tailed data, using a generalized EM algorithm to handle intractability and missing data, demonstrated on synthetic and financial datasets.

Contribution

It proposes a novel GEM-based algorithm for robustly estimating factor analysis parameters under heavy-tailed distributions with missing data.

Findings

Effective in handling heavy-tailed distributions

Robust to missing data

Performs well on synthetic and real financial data

Abstract

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.