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Edgeworth expansions for studentized and prepivoted sample quantiles

Author

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  • Falk, Michael
  • Janas, Daniel

Abstract

Edgeworth expansions of length two are established for the sample quantile, preprivoted by a smoothed bootstrap, and for a studentized sample quantile, where we studentize by means of a kernel density estimate. As a consequence, it turns out that that two-sides confidence intervals for the underlying quantile which are based on these approaches have essentially equal coverage probabilities with level errors being of order o(n-), where n is the sample size. The smoothed bootstrap therefore outperforms competitors such as the percentile method or sign test method which have level errors only of order O(n-). In case of one-sided confidence intervals, the smoothed bootstrap is superior to studentization if and only if the derivative of the underlying density at the quantile is positive. Ams 1980 Subject Classifications: Primary 62E20; Secondary 62G15

Suggested Citation

  • Falk, Michael & Janas, Daniel, 1992. "Edgeworth expansions for studentized and prepivoted sample quantiles," Statistics & Probability Letters, Elsevier, vol. 14(1), pages 13-24, May.
    • Handle: RePEc:eee:stapro:v:14:y:1992:i:1:p:13-24
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    Cited by:

    1. Lavergne, Pascal & Bertail, Patrice, 2020. "Bootstrapping Quasi Likelihood Ratio Tests under Misspecification," TSE Working Papers 20-1102, Toulouse School of Economics (TSE).

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