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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 in parametric statistics. [1]
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.
The maximal information coefficient uses binning as a means to apply mutual information on continuous random variables. Binning has been used for some time as a way of applying mutual information to continuous distributions; what MIC contributes in addition is a methodology for selecting the number of bins and picking a maximum over many possible grids.
The Passing-Bablok procedure fits the parameters and of the linear equation = + using non-parametric methods. The coefficient b {\displaystyle b} is calculated by taking the shifted median of all slopes of the straight lines between any two points, disregarding lines for which the points are identical or b = − 1 {\displaystyle b=-1} .
The input consists of the k closest training examples in a data set. The neighbors are taken from a set of objects for which the class (for k-NN classification) or the object property value (for k-NN regression) is known. This can be thought of as the training set for the algorithm, though no explicit training step is required.
Bootstrapping can be interpreted in a Bayesian framework using a scheme that creates new data sets through reweighting the initial data. Given a set of data points, the weighting assigned to data point in a new data set is =, where is a low-to-high ordered list of uniformly distributed random numbers on [,], preceded by 0 and succeeded by 1.
Since it is a nonparametric method, the Kruskal–Wallis test does not assume a normal distribution of the residuals, unlike the analogous one-way analysis of variance. If the researcher can make the assumptions of an identically shaped and scaled distribution for all groups, except for any difference in medians, then the null hypothesis is ...
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]