An approximation method to derive confidence intervals for quantiles with some applications

An approximation method to derive confidence intervals for quantiles with some applications Standard jackknife confidence intervals for a quantile Q y (β) are usually preferred to confidence intervals based on analytical variance estimators due to their operational simplicity. However, the standard jackknife confidence intervals can give undesirable coverage probabilities for small samples sizes and large or small values of β. In this paper confidence intervals for a population quantile based on several existing estimators of a quantile are derived. These intervals are based on an approximation for the cumulative distribution function of a studentized quantile estimator. Confidence intervals are empirically evaluated by using real data and some applications are illustrated. Results derived from simulation studies show that proposed confidence intervals are narrower than confidence intervals based on the standard jackknife technique, which assumes normal approximation. Proposed confidence intervals also achieve coverage probabilities above to their nominal level. This study indicates that the proposed method can be an alternative to the asymptotic confidence intervals, which can be unknown in practice, and the standard jackknife confidence intervals, which can have poor coverage probabilities and give wider intervals. Quality & Quantity Springer Journals

An approximation method to derive confidence intervals for quantiles with some applications

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Springer Netherlands
Copyright © 2011 by Springer Science+Business Media B.V.
Social Sciences; Methodology of the Social Sciences; Social Sciences, general
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