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Maximum product of spacings prediction of future record values

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  • Grigoriy Volovskiy

    (RWTH Aachen University)

  • Udo Kamps

    (RWTH Aachen University)

Abstract

A spacings-based prediction method for future upper record values is proposed as an alternative to maximum likelihood prediction. For an underlying family of distributions with continuous cumulative distribution functions, the general form of the predictor as a function of the estimator of the distributional parameters is established. A connection between this method and the maximum observed likelihood prediction procedure is shown. The maximum product of spacings predictor turns out to be useful to predict the next record value in contrast to likelihood-based procedures, which provide trivial predictors in this particular case. Moreover, examples are given for the exponential and the Pareto distributions, and a real data set is analyzed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:7:d:10.1007_s00184-020-00767-1
    DOI: 10.1007/s00184-020-00767-1
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Yongzhao Shao & Marjorie Hahn, 1999. "Strong Consistency of the Maximum Product of Spacings Estimates with Applications in Nonparametrics and in Estimation of Unimodal Densities," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(1), pages 31-49, March.
    4. Anatolyev, Stanislav & Kosenok, Grigory, 2005. "An Alternative To Maximum Likelihood Based On Spacings," Econometric Theory, Cambridge University Press, vol. 21(2), pages 472-476, April.
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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. 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.
    3. Stepanov, Alexei & Dembińska, Anna, 2022. "Limit theorems for the uppermost mth spacing based on weak geometric records," Statistics & Probability Letters, Elsevier, vol. 183(C).
    4. Liang Wang & Sanku Dey & Yogesh Mani Tripathi, 2022. "Classical and Bayesian Inference of the Inverse Nakagami Distribution Based on Progressive Type-II Censored Samples," Mathematics, MDPI, vol. 10(12), pages 1-18, June.

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