A new distribution-free quantile estimator

Abstract

A new distribution-free estimator Qp of the pth population quantile is formulated, where Qp is a linear combination of order statistics admitting a jackknife variance estimator having excellent properties. The small sample efficiency of Qp is studied under a variety of light and heavy-tailed symmetric and asymmetric distributions. For the distributions and values of p studied, Qp is generally substantially more efficient than the traditional estimator based on one or two order statistics.

Reference

Frank E Harrell, C E Davis “A new distribution-free quantile estimator” (1982) DOI: 10.1093/biomet/69.3.635

@Article{harrell1982,
  title = {A new distribution-free quantile estimator},
  volume = {69},
  issn = {0006-3444},
  url = {https://academic.oup.com/biomet/article/69/3/635/221346},
  doi = {10.1093/biomet/69.3.635},
  abstract = {A new distribution-free estimator Qp of the pth population quantile is formulated, where Qp is a linear combination of order statistics admitting a jackknife variance estimator having excellent properties. The small sample efficiency of Qp is studied under a variety of light and heavy-tailed symmetric and asymmetric distributions. For the distributions and values of p studied, Qp is generally substantially more efficient than the traditional estimator based on one or two order statistics.},
  language = {en},
  number = {3},
  urldate = {2020-07-14},
  journal = {Biometrika},
  author = {Harrell, Frank E and Davis, C E},
  month = {dec},
  year = {1982},
  note = {Publisher: Oxford Academic},
  pages = {635--640}
}