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Simultaneous prediction regions
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  • Published: June 1992

Simultaneous prediction regions

  • Rudolf Beran1 

Probability Theory and Related Fields volume 92, pages 231–246 (1992)Cite this article

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  • 3 Citations

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Summary

Two new methods for constructing simultaneous prediction regions are the subject of this article. Both methods simultaneously assert a collection of prediction regions, one prediction region for each future observable of interest. Both methods have the same aims: to control the overall coverage probability of the simultaneous prediction region and to keep equal the coverage probabilities of the individual prediction statements that make up the simultaneous region. The latter property is called balance.

The two approaches differ in their choice of critical values. For leading cases, the first method achieves the desired overall coverage probability and the desired balance up to errors of ordern −1, wheren is the size of the learning sample. The second method reduces both errors to ordern −2. Calculating critical values in the second approach usually relies on a bootstrap algorithm.

If overall coverage probability and degree of balance are instead calculatedconditionally given the learning sample, the two methods show the same asymptotic performance. This result reflects intrinsic limits on the extent to which conditional coverage probabilities can be controlled in prediction.

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References

  • Beran, R.: Balanced simultaneous confidence sets. J. Am. Stat. Assoc.83, 679–697 (1988)

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  • Beran, R.: Calibrating prediction regions. J. Am. Stat. Assoc.85, 715–723 (1990)

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  • Beran, R.: Controlling conditional coverage probability in prediction. Ann. Stat.20, (to appear)

  • Box, G.E.P., Jenkins, G.M.: Time series analysis: forecasting and control. Oakland: Hoiden-Day 1976

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  • Carroll, R.J., Ruppert, D.: Prediction and tolerance intervals with transformation and/of weighting. (unpublished preprint, 1989)

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Author information

Authors and Affiliations

  1. Department of Statistics, University of California, 94720, Berkeley, CA, USA

    Rudolf Beran

Authors
  1. Rudolf Beran
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Additional information

This research was supported in part by NSF Grant DMS-87-01426. Part of the work was done while the author was a guest of Sonderforschungsbereich 123 at Universität Heidelberg

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Cite this article

Beran, R. Simultaneous prediction regions. Probab. Th. Rel. Fields 92, 231–246 (1992). https://doi.org/10.1007/BF01194922

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  • Received: 23 August 1990

  • Revised: 23 October 1991

  • Issue Date: June 1992

  • DOI: https://doi.org/10.1007/BF01194922

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Coverage Probability
  • Prediction Statement
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