Universal Prediction for Indexed Classes of Sources

We study universal prediction w.r.t. an indexed class of sources (e.g., parametric families) and general loss functions. We explore the centrality of the self-information loss function (log-loss) in the theory of universal prediction by showing that under certain assumptions, the feasibility of universal prediction w.r.t. the log-loss function, over an indexed class of sources (that is, universal data compression), is a necessary and su cient condition for its feasibility w.r.t. other loss functions.