View source for Non-parametric test

{{TEX|done}}
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]].

====References====
<table>
<TR><TD valign="top">[1]</TD> <TD valign="top">  C.R. Rao,   "Linear statistical inference and its applications" , Wiley  (1965)</TD></TR>
<TR><TD valign="top">[2]</TD> <TD valign="top">  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)</TD></TR>
<TR><TD valign="top">[3]</TD> <TD valign="top">  I.A. Ibragimov,   R.Z. [R.Z. Khas'minskii] Has'minskii,   "Statistical estimation: asymptotic theory" , Springer  (1981)  (Translated from Russian)</TD></TR>
<TR><TD valign="top">[4]</TD> <TD valign="top">  M.G. Kendall,   A. Stuart,   "The advanced theory of statistics" , '''2. Inference and relationship''' , Griffin  (1979)</TD></TR>
</table>