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A composite quantile function estimator with applications in bootstrapping

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  • Alan Hutson

Abstract

In this note we define a composite quantile function estimator in order to improve the accuracy of the classical bootstrap procedure in small sample setting. The composite quantile function estimator employs a parametric model for modelling the tails of the distribution and uses the simple linear interpolation quantile function estimator to estimate quantiles lying between 1/(n+1) and n/(n+1). The method is easily programmed using standard software packages and has general applicability. It is shown that the composite quantile function estimator improves the bootstrap percentile interval coverage for a variety of statistics and is robust to misspecification of the parametric component. Moreover, it is also shown that the composite quantile function based approach surprisingly outperforms the parametric bootstrap for a variety of small sample situations.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:27:y:2000:i:5:p:567-577
    DOI: 10.1080/02664760050076407
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    1. Jiménez Gamero, M. D. & Muñoz García, J. & Muñoz Reyes, A., 1998. "Bootstrapping statistical functionals," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 229-236, August.
    2. Warren Gilchrist, 1997. "Modelling with quantile distribution functions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(1), pages 113-122.
    3. 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.
    4. Mudholkar, Govind S. & Hutson, Alan D., 1997. "Asymmetric quasimedians: Remarks on an anomaly," Statistics & Probability Letters, Elsevier, vol. 32(3), pages 261-268, March.
    5. 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.
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