# International Encyclopedia of Statistical Science

2011 Edition
| Editors: Miodrag Lovric

# Nonparametric Statistical Inference

• Jean Dickinson Gibbons
• Subhabrata Chakraborti
Reference work entry
DOI: https://doi.org/10.1007/978-3-642-04898-2_420

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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