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An Edgeworth expansion for the m out of n bootstrapped median

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Listed:
  • Sakov, Anat
  • Bickel, Peter J.

Abstract

It is well known that the ordinary bootstrap distribution of the median is consistent. We show that for bootstrap samples of size m, an Edgeworth expansion holds with reminder term . With extrapolation this gives a best possible rate estimate of the distribution.

Suggested Citation

  • Sakov, Anat & Bickel, Peter J., 2000. "An Edgeworth expansion for the m out of n bootstrapped median," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 217-223, September.
    • Handle: RePEc:eee:stapro:v:49:y:2000:i:3:p:217-223
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    3. Lee, Chi-Chuan & Yu, Chin-Hsien & Zhang, Jian, 2023. "Heterogeneous dependence among cryptocurrency, green bonds, and sustainable equity: New insights from Granger-causality in quantiles analysis," International Review of Economics & Finance, Elsevier, vol. 87(C), pages 99-109.
    4. Escanciano, Juan Carlos & Velasco, Carlos, 2010. "Specification tests of parametric dynamic conditional quantiles," Journal of Econometrics, Elsevier, vol. 159(1), pages 209-221, November.
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    6. Miguel Arcones, 2003. "On the asymptotic accuracy of the bootstrap under arbitrary resampling size," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 563-583, September.
    7. Bechir Raggad & Elie Bouri, 2023. "Quantile Dependence between Crude Oil Returns and Implied Volatility: Evidence from Parametric and Nonparametric Tests," Mathematics, MDPI, vol. 11(3), pages 1-23, January.
    8. Lee, Chi-Chuan & Lee, Chien-Chiang, 2020. "Insurance activity, real output, and geopolitical risk: Fresh evidence from BRICS," Economic Modelling, Elsevier, vol. 92(C), pages 207-215.
    9. Escanciano, Juan Carlos & Jacho-Chávez, David T., 2010. "Approximating the critical values of Cramér-von Mises tests in general parametric conditional specifications," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 625-636, March.
    10. Ahmed Ali & Granberg Mark & Uddin Gazi Salah & Troster Victor, 2022. "Asymmetric dynamics between uncertainty and unemployment flows in the United States," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 26(1), pages 155-172, February.
    11. Si Mohammed, K. & Mellit, A., 2023. "The relationship between oil prices and the indices of renewable energy and technology companies based on QQR and GCQ techniques," Renewable Energy, Elsevier, vol. 209(C), pages 97-105.
    12. Lyubchich, Vyacheslav & Wang, Xingyu & Heyes, Andrew & Gel, Yulia R., 2016. "A distribution-free m-out-of-n bootstrap approach to testing symmetry about an unknown median," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 1-9.
    13. Gatfaoui, Hayette, 2017. "Equity market information and credit risk signaling: A quantile cointegrating regression approach," Economic Modelling, Elsevier, vol. 64(C), pages 48-59.
    14. Matos, Paulo & Costa, Antonio & da Silva, Cristiano, 2021. "COVID-19, stock market and sectoral contagion in US: a time-frequency analysis," Research in International Business and Finance, Elsevier, vol. 57(C).
    15. Mighri, Zouheir & Ragoubi, Hanen & Sarwar, Suleman & Wang, Yihan, 2022. "Quantile Granger causality between US stock market indices and precious metal prices," Resources Policy, Elsevier, vol. 76(C).
    16. Hiroaki Kaido & Kaspar Wüthrich, 2021. "Decentralization estimators for instrumental variable quantile regression models," Quantitative Economics, Econometric Society, vol. 12(2), pages 443-475, May.
    17. Troster, Victor & Shahbaz, Muhammad & Uddin, Gazi Salah, 2018. "Renewable energy, oil prices, and economic activity: A Granger-causality in quantiles analysis," Energy Economics, Elsevier, vol. 70(C), pages 440-452.
    18. Andisheh Saliminezhad & Pejman Bahramian, 2021. "The role of financial stress in the economic activity: Fresh evidence from a Granger‐causality in quantiles analysis for the UK and Germany," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 1670-1680, April.
    19. Escanciano, J.C. & Goh, S.C., 2014. "Specification analysis of linear quantile models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 495-507.
    20. Juan Carlos Escanciano & Chuan Goh, 2010. "Specification Analysis of Structural Quantile Regression Models," Working Papers tecipa-415, University of Toronto, Department of Economics.

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