  Compositional data are multivariate observations that carry only relative
information between components. Applying standard multivariate statistical
methodology directly to analyze compositional data can lead to paradoxes and
misinterpretations. Compositional data also frequently appear in insurance,
especially with telematics information. However, such type of data does not
receive deserved special treatment in most existing actuarial literature. In
this paper, we explore and investigate the use of exponential family principal
component analysis (EPCA) to analyze compositional data in insurance. The
method is applied to analyze a dataset obtained from the U.S. Mine Safety and
Health Administration. The numerical results show that EPCA is able to produce
principal components that are significant predictors and improve the prediction
accuracy of the regression model. The EPCA method can be a promising useful
tool for actuaries to analyze compositional data.
