An approximation method to derive confidence intervals for quantiles with some applications |
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Authors: | M Rueda A Arcos I Sánchez-Borrego J F Muñoz |
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Institution: | 1.Department of Statistics and Operational Research,University of Granada,Granada,Spain;2.University of Granada,Granada,Spain |
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Abstract: | 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. |
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Keywords: | |
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