ArticleOriginal scientific text

Title

Estimating median and other quantiles in nonparametric models

Authors 1

Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, P.O. Box 137, 00-950 Warszawa, Poland

Abstract

Though widely accepted, in nonparametric models admitting asymmetric distributions the sample median, if n=2k, may be a poor estimator of the population median. Shortcomings of estimators which are not equivariant are presented.

Keywords

estimation, quantiles, median

Bibliography

  1. P. J. Bickel and K. A. Doksum (1977), Mathematical Statistics. Basic Ideas and Selected Topics, Holden-Day.
  2. B. M. Brown (1985), Median estimates and sign tests, in: Encyclopedia of Statistical Sciences, Vol. 5, Wiley.
  3. C. E. Davis and S. M. Steinberg (1985), Quantile estimation, in: Encyclopedia of Statistical Sciences, Vol. 7, Wiley.
  4. S. T. Gross (1985), Median estimation, inverse, in: Encyclopedia of Statistical Sciences, Vol. 5, Wiley.
  5. F. E. Harrell and C. E. Davis (1982), A new distribution-free quantile estimator, Biometrika 69, 635-640.
  6. W. D. Kaigh and P. A. Lachenbruch (1982), A generalized quantile estimator, Comm. Statist. Theory Methods 11, 2217-2238.
  7. E. L. Lehmann (1983), Theory of Point Estimation, Wiley.
  8. W. Uhlmann (1963), Ranggrössen als Schätzfunktionen, Metrika 7 (1), 23-40.
  9. R. Zieliński (1988), A distribution-free median-unbiased quantile estimator, Statistics 19 (2), 223-227.
Pages:
363-370
Main language of publication
English
Received
1995-05-18
Published
1995
Exact and natural sciences