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Approximate repeated-measures shrinkage

Author

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  • Brentnall, Adam R.
  • Crowder, Martin J.
  • Hand, David J.

Abstract

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.

Suggested Citation

  • Brentnall, Adam R. & Crowder, Martin J. & Hand, David J., 2011. "Approximate repeated-measures shrinkage," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1150-1159, February.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:2:p:1150-1159
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    References listed on IDEAS

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    1. Adam R. Brentnall & Martin J. Crowder & David J. Hand, 2008. "A statistical model for the temporal pattern of individual automated teller machine withdrawals," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(1), pages 43-59.
    2. 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.
    3. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    4. 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.
    5. Laird, Nan M. & Louis, Thomas A., 1991. "Smoothing the non-parametric estimate of a prior distribution by roughening : A computational study," Computational Statistics & Data Analysis, Elsevier, vol. 12(1), pages 27-37, August.
    6. 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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