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.
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- Brian S. Caffo & Wolfgang Jank & Galin L. Jones, 2005. "Ascent-based Monte Carlo expectation- maximization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 235-251.
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- An, Lihua & Nkurunziza, Sévérien & Fung, Karen Y. & Krewski, Daniel & Luginaah, Isaac, 2009. "Shrinkage estimation in general linear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2537-2549, May.
- Yong Wang, 2007. "On fast computation of the non-parametric maximum likelihood estimate of a mixing distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 185-198.
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