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Sharp distribution-free bounds on the bias in estimating quantiles via order statistics

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  • Okolewski, Andrzej
  • Rychlik, Tomasz

Abstract

Sharp distribution-free lower and upper bounds on the bias in estimating quantiles by the sample counterparts are obtained by the use of Moriguti's greatest convex minorant approach.

Suggested Citation

  • Okolewski, Andrzej & Rychlik, Tomasz, 2001. "Sharp distribution-free bounds on the bias in estimating quantiles via order statistics," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 207-213, April.
    • Handle: RePEc:eee:stapro:v:52:y:2001:i:2:p:207-213
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    References listed on IDEAS

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    1. Gajek, Leslaw & Rychlik, Tomasz, 1998. "Projection Method for Moment Bounds on Order Statistics from Restricted Families, : II. Independent Case," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 156-182, February.
    2. Zielinski, Ryszard, 1998. "Uniform strong consistency of sample quantiles," Statistics & Probability Letters, Elsevier, vol. 37(2), pages 115-119, February.
    3. Zielinski, Ryszard, 1999. "Best equivariant nonparametric estimator of a quantile," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 79-84, October.
    4. Cheng, Cheng, 1995. "The Bernstein polynomial estimator of a smooth quantile function," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 321-330, September.
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    Cited by:

    1. Strzalkowska-Kominiak, Ewa & Cao, Ricardo, 2013. "Maximum likelihood estimation for conditional distribution single-index models under censoring," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 74-98.
    2. Ann-Kristin Kreutzmann, 2018. "Estimation of sample quantiles: challenges and issues in the context of income and wealth distributions [Die Schätzung von Quantilen: Herausforderungen und Probleme im Kontext von Einkommens- und V," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 12(3), pages 245-270, December.
    3. Thomas Blanchet & Ignacio Flores & Marc Morgan, 2022. "The weight of the rich: improving surveys using tax data," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(1), pages 119-150, March.
    4. Mariusz Bieniek & Luiza Pańczyk, 2023. "On the choice of the optimal single order statistic in quantile estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(2), pages 303-333, April.
    5. Soonwoo Kwon, 2023. "Optimal Shrinkage Estimation of Fixed Effects in Linear Panel Data Models," Papers 2308.12485, arXiv.org, revised Oct 2023.

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