Prediction and Sufficiency in the Model of Factor Analysis

We contrast two approaches to the prediction of latent variables in the model of factor analysis. The likelihood statistic constitutes the set of minimal sufficient statistics for the unobservables when sampling arises from the exponential family of distributions. Linear predictors on the other hand can be obtained as distribution-free statistics. The paper provides conditions under which a class of linear predictors is sufficient for the exponential family of distributions.