Definition:Nonparametric Method
Definition
A nonparametric method is a technique for statistical investigation in which no assumptions are made about any parameters.
Examples
Arbitrary Example $1$
Suppose we have random samples from two populations with unspecified cumulative distribution functions $\map F x$ and $\map G x$.
A test for:
- the hypothesis $\map F x = \map G x$ for all $x$
against:
- the alternative hypothesis that $\map F x < \map G x$ for all $x$
would be a test that is both nonparametric and distribution-free.
Arbitrary Example $2$
Suppose we have random samples from two populations with unspecified cumulative distribution functions $\map F x$ and $\map G x$.
A test for:
- the hypothesis $\map G x = \map F x$ for all $x$
against:
- the alternative hypothesis that $\map G x < \map F {x - \theta}$ for all $x$, where $\theta$ is some parameter
would be a test that is distribution-free but not nonparametric, as it involves a parameter $\theta$.
Also known as
A nonparametric method or nonparametric test is also known as a distribution-free method, but the latter has a wider application and it is advised not to conflate the techniques.
Some sources hyphenate: non-parametric method or non-parametric test.
Also see
- Results about nonparametric methods can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): nonparametric methods
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): nonparametric methods