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The exact bootstrap mean and variance of an L‐estimator

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  • A. D. Hutson
  • M. D. Ernst

Abstract

Exact analytic expressions for the bootstrap mean and variance of any L‐estimator are obtained, thus eliminating the error due to bootstrap resampling. The expressions follow from the direct calculation of the bootstrap mean vector and covariance matrix of the whole set of order statistics. By using these expressions, recommendations can be made about the appropriateness of bootstrap estimation under given conditions.

Suggested Citation

  • A. D. Hutson & M. D. Ernst, 2000. "The exact bootstrap mean and variance of an L‐estimator," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 89-94.
    • Handle: RePEc:bla:jorssb:v:62:y:2000:i:1:p:89-94
    DOI: 10.1111/1467-9868.00221
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    Cited by:

    1. Lauer, Alexandra & Zähle, Henryk, 2017. "Bootstrap consistency and bias correction in the nonparametric estimation of risk measures of collective risks," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 99-108.
    2. Kim, Joseph H.T., 2010. "Bias correction for estimated distortion risk measure using the bootstrap," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 198-205, October.
    3. Hutson, Alan D., 2000. "Estimating the covariance of bivariate order statistics with applications," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 195-203, June.
    4. Diane L. Evans & Lawrence M. Leemis & John H. Drew, 2006. "The Distribution of Order Statistics for Discrete Random Variables with Applications to Bootstrapping," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 19-30, February.
    5. Dimitris Bertsimas & Bradley Sturt, 2020. "Computation of Exact Bootstrap Confidence Intervals: Complexity and Deterministic Algorithms," Operations Research, INFORMS, vol. 68(3), pages 949-964, May.
    6. Gámiz, Maria Luz & Nozal-Cañadas, Rafael & Raya-Miranda, Rocío, 2020. "TTT-SiZer: A graphic tool for aging trends recognition," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    7. Brodin, Erik, 2006. "On quantile estimation by bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 50(6), pages 1398-1406, March.
    8. Michael R. Dugas & Francisco J. Samaniego, 2007. "On optimal system designs in reliability‐economics frameworks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 568-582, August.
    9. Alan Hutson, 2000. "A composite quantile function estimator with applications in bootstrapping," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(5), pages 567-577.
    10. Alan Hutson, 2009. "A distribution function estimator for the difference of order statistics from two independent samples," Statistical Papers, Springer, vol. 50(1), pages 203-208, January.
    11. Elamir, Elsayed A. H. & Seheult, Allan H., 2003. "Trimmed L-moments," Computational Statistics & Data Analysis, Elsevier, vol. 43(3), pages 299-314, July.
    12. Cseres-Gergely, Zsombor & Kvedaras, Virmantas, 2019. "Change and convergence of income distributions in the European Union during 2007-2014," Working Papers 2019-13, Joint Research Centre, European Commission.
    13. Gabriel Montes Rojas & Andrés Sebastián Mena, 2020. "Density estimation using bootstrap quantile variance and quantile-mean covariance," Documentos de trabajo del Instituto Interdisciplinario de Economía Política IIEP (UBA-CONICET) 2020-50, Universidad de Buenos Aires, Facultad de Ciencias Económicas, Instituto Interdisciplinario de Economía Política IIEP (UBA-CONICET).
    14. Álvarez, Adolfo & Peña, Daniel, 2009. "Recombining dependent data: an Order Statistics," DES - Working Papers. Statistics and Econometrics. WS ws098526, Universidad Carlos III de Madrid. Departamento de Estadística.
    15. Modarres, Reza & Hui, Terrence P. & Zheng, Gang, 2006. "Resampling methods for ranked set samples," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1039-1050, November.
    16. Kvedaras, Virmantas & Cseres-Gergely, Zsombor, 2020. "Convergence of income distributions: Total and inequality-affecting changes in the EU," Economics Letters, Elsevier, vol. 188(C).

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