We show that, for discrete exponential families, the sample mean of n observations does not stochastically dominate a single observation when estimating the population mean. This is in stark contrast to the case of a normal distribution.

We consider stochastic domination in predictive density estimation problems when the underlying loss metric is α-divergence, D(α), loss introduced by Csiszàr (1967). The underlying distributions considered are normal location-scale models, including the distribution of the observables, the...