Bayesian shrinkage estimates and forecasts of individual and total or aggregate outcomes

Bayesian shrinkage à la Stein and others can improve estimation of individual parameters and forecasts of individual future outcomes. In this paper the issue of the impact of shrinkage on the estimation of sums or totals of individual parameters and of individual outcomes is analyzed. Quadratic and “balanced” loss functions will be employed. The latter are a linear combination of “goodness of fit” and “precision of estimation” loss functions. Several examples will be analyzed in detail to illustrate general principles.