International Encyclopedia of Statistical Science

2011 Edition
| Editors: Miodrag Lovric

Nonparametric Statistical Inference

  • Jean Dickinson Gibbons
  • Subhabrata Chakraborti
Reference work entry

Nonparametric statistical inference is a collective term given to inferences thatare valid under less restrictive assumptions than with classical (parametric)statistical inference. The assumptions that can be relaxed include specifying theprobability distribution of the population from which the sample was drawn andthe level of measurement required of the sample data. For example, wemay have to assume that the population is symmetric, which is much lessrestrictive than assuming the population is the normal distribution. Thedata may be ratings or ranks, i.e., measurements on an ordinal scale,instead of precise measurements on an interval or ratio scale. Or the datamay be counts. In nonparametric inference, the null distribution of thestatistic on which the inference is based does not depend on the probabilitydistribution of the population from which the sample was drawn. In otherwords, the statistic has the same sampling distribution under the nullhypothesis, irrespective of the form...

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References and Further Reading

  1. Bradley JV (1968) Distribution-free statistical tests. Prentice-Hall, Englewood CliffszbMATHGoogle Scholar
  2. Gibbons JD, Chakraborti S (2010) Nonparametric statistical inference, 5th edn. Taylor & Francis/CRC Press, Boca RatonGoogle Scholar
  3. Kendall MG, Gibbons JD (1990) Rank correlation methods. 5th edn. Edward Arnold, LondonzbMATHGoogle Scholar
  4. Noether GE (1967) Elements of noparametric statistics. Wiley, New YorkGoogle Scholar
  5. Pratt JW, Gibbons JD (1981) Concepts of nonparametric theory. Springer, New YorkzbMATHGoogle Scholar
  6. Savage IR (1962) Bibliography of nonparametric statistics. Harvard University Press, CambridgeGoogle Scholar
  7. Walsh JE (1962) Handbook of nonparametric statistics, I: Investigation of randomness, moments, percentiles, and distribution. Van Nostrand, New YorkGoogle Scholar
  8. Walsh JE (1965) Handbook of nonparametric statistics, II: Results for two and several sample problems, symmetry and extremes. Van Nostrand, New YorkzbMATHGoogle Scholar
  9. Walsh JE (1968) Handbook of nonparametric statistics, III: Analysis of variance. Van Nostrand, New YorkzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jean Dickinson Gibbons
    • 1
  • Subhabrata Chakraborti
    • 2
  1. 1.The University of AlabamaTuscaloosaUSA
  2. 2.The University of AlabamaTuscaloosaUSA