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Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as is parametric statistics. [1]
Nonparametric models are therefore also called distribution free. Nonparametric (or distribution-free) inferential statistical methods are mathematical procedures for statistical hypothesis testing which, unlike parametric statistics, make no assumptions about the frequency distributions of the variables being assessed.
Nonparametric regression is a category of regression analysis in which the predictor does not take a predetermined form but is constructed according to information derived from the data. That is, no parametric equation is assumed for the relationship between predictors and dependent variable.
Assumptions, parametric and non-parametric: There are two groups of statistical tests, parametric and non-parametric. The choice between these two groups needs to be justified. The choice between these two groups needs to be justified.
In statistics, the k-nearest neighbors algorithm (k-NN) is a non-parametric supervised learning method. It was first developed by Evelyn Fix and Joseph Hodges in 1951, [1] and later expanded by Thomas Cover. [2] Most often, it is used for classification, as a k-NN classifier, the output of which is a class membership
Algorithms of this nature use statistical inference to find the best class for a given instance. Unlike other algorithms, which simply output a "best" class, probabilistic algorithms output a probability of the instance being a member of each of the possible classes. The best class is normally then selected as the one with the highest probability.
Permutation tests are a subset of non-parametric statistics. Assuming that our experimental data come from data measured from two treatment groups, the method simply generates the distribution of mean differences under the assumption that the two groups are not distinct in terms of the measured variable.
The estimation method requires that the data are independent and identically distributed (iid). It performs well even when the distribution is asymmetric or censored. [1] EL methods can also handle constraints and prior information on parameters. Art Owen pioneered work in this area with his 1988 paper. [2]