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High-order coverage of smoothed Bayesian bootstrap intervals for population quantiles

Author

Listed:
  • David M. Kaplan

    (Department of Economics, University of Missouri)

  • Lonnie Hofmann

    (Department of Economics, University of Missouri)

Abstract

We characterize the high-order coverage accuracy of smoothed and unsmoothed Bayesian bootstrap confidence intervals for population quantiles. Although the original (Rubin, 1981) unsmoothed intervals have the same O(n^{-1/2}) coverage error as the standard empirical bootstrap, the smoothed Bayesian bootstrap of Banks (1988) has much smaller O(n^{-3/2}[log(n)]^3) coverage error and is exact in special cases, without requiring any smoothing parameter. It automatically removes an error term of order 1/n that other approaches need to explicitly correct for. This motivates further study of the smoothed Bayesian bootstrap in more complex settings and models.

Suggested Citation

  • David M. Kaplan & Lonnie Hofmann, 2020. "High-order coverage of smoothed Bayesian bootstrap intervals for population quantiles," Working Papers 2012, Department of Economics, University of Missouri.
    • Handle: RePEc:umc:wpaper:2012
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    References listed on IDEAS

    as
    1. Goldman, Matt & Kaplan, David M., 2017. "Fractional order statistic approximation for nonparametric conditional quantile inference," Journal of Econometrics, Elsevier, vol. 196(2), pages 331-346.
    2. Hahn, Jinyong, 1997. "Bayesian Bootstrap of the Quantile Regression Estimator: A Large Sample Study," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(4), pages 795-808, November.
    3. David M. Kaplan & Matt Goldman, 2015. "Nonparametric inference on conditional quantile differences and linear combinations, using L-statistics," Working Papers 1503, Department of Economics, University of Missouri.
    4. Matt Goldman & David M. Kaplan, 2018. "Non‐parametric inference on (conditional) quantile differences and interquantile ranges, using L‐statistics," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 136-169, June.
    5. Hall, Peter & Martin, Michael A., 1989. "A note on the accuracy of bootstrap percentile method confidence intervals for a quantile," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 197-200, August.
    6. Alan Hutson, 1999. "Calculating nonparametric confidence intervals for quantiles using fractional order statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(3), pages 343-353.
    7. Meeden, Glen, 1993. "Noninformative nonparametric Bayesian estimation of quantiles," Statistics & Probability Letters, Elsevier, vol. 16(2), pages 103-109, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    continuity correction; credible intervals; fractional order statistics;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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