 Nonparametric statistics

Nonparametric statistics studies statistical inference without restricting the unknown probability distribution or target function to a fixed finite-dimensional parametric statistical model. In density estimation and nonparametric regression, the number of features that an estimator can represent may grow with the sample size. Rank tests offer another approach: the probability distribution of their test statistic under the null hypothesis can be obtained without specifying the common continuous probability distribution.

"Nonparametric" does not mean free of assumptions or tuning choices. A kernel density estimator still requires a kernel for density estimation and a smoothing bandwidth, and its interpretation depends on assumptions about the statistical sample. The freedom is useful when a prescribed shape, such as a single normal distribution, would hide features that the observations might reveal.

Nonparametric statistics refers to a branch of statistics that does not assume a specific distribution for the population from which the samples are drawn. Unlike parametric methods, which rely on assumptions about the parameters (such as mean and variance) of a population's distribution (often assuming a normal distribution), nonparametric methods are more flexible as they can be used with data that do not meet these assumptions.