# Non-parametric test

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A statistical test of a hypothesis : against the alternative : when at least one of the two parameter sets and is not topologically equivalent to a subset of a Euclidean space. Apart from this definition there is also another, wider one, according to which a statistical test is called non-parametric if the statistical inferences obtained using it do not depend on the particular null-hypothesis probability distribution of the observable random variables on the basis of which one wants to test against . In this case, instead of the term "non-parametric test" one speaks frequently of a "distribution-free statistical testdistribution-free test" . The Kolmogorov test is a classic example of a non-parametric test. See also Non-parametric methods in statistics; Kolmogorov–Smirnov test.

#### References

 [1] C.R. Rao, "Linear statistical inference and its applications" , Wiley (1965) [2] L.N. Bol'shev, N.V. Smirnov, "Tables of mathematical statistics" , Libr. math. tables , 46 , Nauka (1983) (In Russian) (Processed by L.S. Bark and E.S. Kedrova) [3] I.A. Ibragimov, R.Z. [R.Z. Khas'minskii] Has'minskii, "Statistical estimation: asymptotic theory" , Springer (1981) (Translated from Russian) [4] M.G. Kendall, A. Stuart, "The advanced theory of statistics" , 2. Inference and relationship , Griffin (1979)
How to Cite This Entry:
Non-parametric test. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Non-parametric_test&oldid=15131
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article