Advanced search
Publication Cover
Communications in Statistics - Theory and Methods Volume 38, 2009 - Issue 7
Submit an article Journal homepage
188
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

Optimal Nonparametric Quantile Estimators. Towards a General Theory. A Survey

Ryszard Zieliński Department of Mathematical Statistics, Institute of Mathematics, Polish Academy of Science, Warszawa, PolandCorrespondence[email protected]
Pages 980-992 | Received 06 Mar 2008, Accepted 17 Jul 2008, Published online: 19 Mar 2009

References

  • Bickel , P. J. , Lehmann , E. L. ( 1975–1979 ). Descriptive statistics for nonparametric models. I–III . Ann. Statist . 3:1038–1045, 1045–1069; 4:1139–1158; IV Contribution to Statistics: Hájek Memorial Volume . Jureckova , J. ed. Prague : Academia , pp. 33 – 40 .
  • Davis , C. E. , Steinberg , S. M. ( 1986 ). Quantile estimation . Encyclopedia of Statistical Sciences , Vol. 7 . New York : Wiley .
  • Harrell , F. E. , Davis , C. E. ( 1982 ). A new distribution-free quantile estimator . Biometrika 69 : 635 – 640 .
  • Kaigh , W. D. , Lachenbruch , P. A. ( 1982 ). A generalized quantile estimator . Commun. Statist. Theor. Meth. 12 : 2427 – 2443 .
  • Kaigh , W. D. , Cheng , C. ( 1991 ). Subsampling quantile estimators and uniformity criteria . Commun. Statist. Theor. Meth. 20 : 539 – 560 .
  • Keating , J. P. , Tripathi , R. C. ( 1986 ). Percentiles, Estimation of Encyclopedia of Statistical Sciences . Vol. 7 , New York : Wiley .
  • Keating , J. P. , Mason , R. L. , Sen , P. K. ( 1993 ). Pitman's Measure of Closeness: A Comparison of Statistical Estimators . Philadelphia : SIAM .
  • Lehmann , E. L. ( 1983 ). Theory of Point Estimation . New York : Wiley .
  • Rao , C. R. ( 1973 ). Linear Statistical Inference and its Applications . 2nd ed. New York : Wiley .
  • Reiss , R.-D. ( 1989 ). Approximate Distributions of Order Statistics with Applications to Nonparametric Statistics . New York : Springer-Verlag .
  • Uhlmann , W. ( 1963 ). Ranggrössen als Schätzfunktionen . Metrika 7 ( 1 ): 23 – 40 .
  • Zieliński , R. ( 1988 ). A distribution-free median-unbiased quantile estimator . Statistics 19 : 223 – 227 .
  • Zieliński , R. ( 1995 ). Estimating median and other quantiles in nonparametric models. 23.3:363–370. Correction : Applications Math . ( 1996 ) 23.4 : 475 .
  • Zieliński , R. ( 1999 ). Best equivariant nonparametric estimator of a quantile . Statist. Probab. Lett. 45 : 79 – 84 .
  • Zieliński , R. ( 2001 ). PMC-optimal nonparametric quantile estimator . Statistics 35 : 453 – 462 .
  • Zieliński , R. ( 2006 ). Small-sample quantile estimators in a large nonparametric model . Commun. Statist. Theory Meth. 35 : 1223 – 1241 .
  • Zieliński , R. ( 2007 ). A sharp inequality for medians of L-statistics in a nonparametric statistical model . JIRSS 6 ( 2 ): 173 – 177 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.