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Maximum observed likelihood prediction of future record values

Author

Listed:
  • Grigoriy Volovskiy

    (RWTH Aachen University)

  • Udo Kamps

    (RWTH Aachen University)

Abstract

Point prediction of future upper record values is considered. For an underlying absolutely continuous distribution with strictly increasing cumulative distribution function, the general form of the predictor obtained by maximizing the observed predictive likelihood function is established. The results are illustrated for the exponential, extreme-value and power-function distributions, and the performance of the obtained predictors is compared to that of maximum likelihood predictors on the basis of the mean squared error and the Pitman’s measure of closeness criteria. For exponential and extreme-value distributions, it is shown that under slight restrictions, the maximum observed likelihood predictor outperforms the maximum likelihood predictor in terms of both performance criteria.

Suggested Citation

  • Grigoriy Volovskiy & Udo Kamps, 2020. "Maximum observed likelihood prediction of future record values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1072-1097, December.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:4:d:10.1007_s11749-020-00701-7
    DOI: 10.1007/s11749-020-00701-7
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    References listed on IDEAS

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    1. Razmkhah, M. & Ahmadi, Jafar, 2013. "Pitman closeness of current k-records to population quantiles," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 148-156.
    2. Jafar Ahmadi & M. Doostparast, 2006. "Bayesian estimation and prediction for some life distributions based on record values," Statistical Papers, Springer, vol. 47(3), pages 373-392, June.
    3. Kaminsky, Kenneth S., 1987. "Prediction of IBNR claim counts by modelling the distribution of report lags," Insurance: Mathematics and Economics, Elsevier, vol. 6(2), pages 151-159, April.
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    Citations

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    Cited by:

    1. Christina Empacher & Udo Kamps & Grigoriy Volovskiy, 2023. "Statistical Prediction of Future Sports Records Based on Record Values," Stats, MDPI, vol. 6(1), pages 1-17, January.
    2. Grigoriy Volovskiy & Udo Kamps, 2020. "Maximum product of spacings prediction of future record values," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(7), pages 853-868, October.
    3. Jorge Navarro, 2022. "Prediction of record values by using quantile regression curves and distortion functions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(6), pages 675-706, August.

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