Non-parametric test

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A statistical test of a hypothesis $H_0$: $\theta\in\Theta_0\subset\Theta$ against the alternative $H_1$: $\theta\in\Theta_1=\Theta\setminus\Theta_0$ when at least one of the two parameter sets $\Theta_0$ and $\Theta_1$ 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 $H_0$ against $H_1$. In this case, instead of the term "non-parametric test" one speaks frequently of a "distribution-free test" . The Kolmogorov test is a classic example of a non-parametric test.

See also Non-parametric methods in statistics; Kolmogorov–Smirnov test.


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[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:
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article