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Omitting Meaningless Digits in Point Estimates: The Probability Guarantee of Leading-Digit Rules

Author

Listed:
  • Wheyming T. Song

    (Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China)

  • Bruce W. Schmeiser

    (School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47907)

Abstract

Motivated by the question of which point-estimator digits to report in a statistical experiment, we study the probabilistic behavior of the digits as a function of the true performance measure and the point estimator's standard error. We investigate the family of Leading-Digit Rules, which guarantees that every unreported digit has correctness probability below a given threshold. Choosing the threshold to be about 0.198 yields Yoneda's rule. The easy-to-implement rule that reports the point estimate through the leading digit of the standard error has threshold (approximately) 0.117, which is not much larger than the one-in-ten probability of a uniformly distributed random digit being correct.

Suggested Citation

  • Wheyming T. Song & Bruce W. Schmeiser, 2009. "Omitting Meaningless Digits in Point Estimates: The Probability Guarantee of Leading-Digit Rules," Operations Research, INFORMS, vol. 57(1), pages 109-117, February.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:1:p:109-117
    DOI: 10.1287/opre.1080.0529
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    Citations

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    Cited by:

    1. Song, Wheyming Tina & Chih, Mingchang, 2013. "Run length not required: Optimal-mse dynamic batch means estimators for steady-state simulations," European Journal of Operational Research, Elsevier, vol. 229(1), pages 114-123.
    2. Tina Song, Wheyming & Lin, Peisyuan, 2018. "System reliability of stochastic networks with multiple reworks," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 258-268.
    3. Yan, Xiangbin & Qiu, Hui & Peng, Rui & Wu, Shaomin, 2020. "Optimal configuration of a power grid system with a dynamic performance sharing mechanism," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    4. Song, Wheyming Tina, 2019. "The Song rule outperforms optimal-batch-size variance estimators in simulation output analysis," European Journal of Operational Research, Elsevier, vol. 275(3), pages 1072-1082.
    5. Song, Wheyming T. & Chih, Mingchang, 2010. "Extended dynamic partial-overlapping batch means estimators for steady-state simulations," European Journal of Operational Research, Elsevier, vol. 203(3), pages 640-651, June.

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