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Improved Prediction Intervals and Distribution Functions

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  • PAOLO VIDONI

Abstract

. The plug‐in solution is usually not entirely adequate for computing prediction intervals, as their coverage probability may differ substantially from the nominal value. Prediction intervals with improved coverage probability can be defined by adjusting the plug‐in ones, using rather complicated asymptotic procedures or suitable simulation techniques. Other approaches are based on the concept of predictive likelihood for a future random variable. The contribution of this paper is the definition of a relatively simple predictive distribution function giving improved prediction intervals. This distribution function is specified as a first‐order unbiased modification of the plug‐in predictive distribution function based on the constrained maximum likelihood estimator. Applications of the results to the Gaussian and the generalized extreme‐value distributions are presented.

Suggested Citation

  • Paolo Vidoni, 2009. "Improved Prediction Intervals and Distribution Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 735-748, December.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:4:p:735-748
    DOI: 10.1111/j.1467-9469.2009.00656.x
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    1. J. F. Lawless & Marc Fredette, 2005. "Frequentist prediction intervals and predictive distributions," Biometrika, Biometrika Trust, vol. 92(3), pages 529-542, September.
    2. Paolo Vidoni, 2009. "A simple procedure for computing improved prediction intervals for autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(6), pages 577-590, November.
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    Cited by:

    1. Yang Liu & Ji Seung Yang, 2018. "Bootstrap-Calibrated Interval Estimates for Latent Variable Scores in Item Response Theory," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 333-354, June.
    2. Eric Beutner & Alexander Heinemann & Stephan Smeekes, 2017. "A Justification of Conditional Confidence Intervals," Papers 1710.00643, arXiv.org, revised Jan 2019.
    3. Paolo Vidoni, 2009. "A simple procedure for computing improved prediction intervals for autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(6), pages 577-590, November.
    4. D. Concordet & R. Servien, 2014. "Individual prediction regions for multivariate longitudinal data with small samples," Biometrics, The International Biometric Society, vol. 70(3), pages 629-638, September.
    5. Vidoni, Paolo, 2015. "Calibrated multivariate distributions for improved conditional prediction," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 16-25.

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