Approximate repeated-measures shrinkage

A general method is formalised for the problem of making predictions for a fixed group of individual units, following a sequence of repeated measures on each. A review of some related work is undertaken and, using some of its terminology, the approach might be described as approximate non-parametric empirical Bayes prediction. It is contended that the method may often produce predictions that are, in practice, comparable or not much worse than more sophisticated methods, but sometimes for a smaller computational cost. Two examples are used to demonstrate the approach, exploring the prediction of baseball averages and spatial–temporal rainfall. The method performs favourably in both examples in comparison with James–Stein, empirical Bayes and other predictions; it also provides a relatively simple and computationally feasible way of determining whether it is worth modelling between-individual variability.