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Improved confidence intervals for quantiles

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  • Yoshihiko Maesono
  • Spiridon Penev

Abstract

We derive the Edgeworth expansion for the studentized version of the kernel quantile estimator. Inverting the expansion allows us to get very accurate confidence intervals for the pth quantile under general conditions. The results are applicable in practice to improve inference for quantiles when sample sizes are moderate. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • Yoshihiko Maesono & Spiridon Penev, 2013. "Improved confidence intervals for quantiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 167-189, February.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:1:p:167-189
    DOI: 10.1007/s10463-012-0369-6
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    References listed on IDEAS

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    1. Daniel Janas, 1993. "A smoothed bootstrap estimator for a studentized sample quantile," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 317-329, June.
    2. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    3. Xiaojing Xiang, 1995. "A Berry-Esseen theorem for the kernel quantile estimator with application to studying the deficiency of quantile estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(2), pages 237-251, June.
    4. Yoshihiko Maesono & Spiridon Penev, 2011. "Edgeworth expansion for the kernel quantile estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 617-644, June.
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    Cited by:

    1. Nadezhda Gribkova & Ričardas Zitikis, 2019. "Weighted allocations, their concomitant-based estimators, and asymptotics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 811-835, August.
    2. Beutner, E. & Cramer, E., 2014. "Using linear interpolation to reduce the order of the coverage error of nonparametric prediction intervals based on right-censored data," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 95-109.

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