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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.
In regression problems, case resampling refers to the simple scheme of resampling individual cases – often rows of a data set. For regression problems, as long as the data set is fairly large, this simple scheme is often acceptable. [citation needed] However, the method is open to criticism [citation needed]. [15]
The naive version of the algorithm is easy to implement by computing the distances from the test example to all stored examples, but it is computationally intensive for large training sets. Using an approximate nearest neighbor search algorithm makes k-NN computationally tractable even for large data sets. Many nearest neighbor search ...
Using the Lagrangian multiplier method to maximize the logarithm of the empirical likelihood subject to the trivial normalization constraint, we find = / as a maximum. Therefore, F ^ {\displaystyle {\hat {F}}} is the empirical distribution function .
Many parametric methods are proven to be the most powerful tests through methods such as the Neyman–Pearson lemma and the Likelihood-ratio test. Another justification for the use of non-parametric methods is simplicity. In certain cases, even when the use of parametric methods is justified, non-parametric methods may be easier to use.
Data envelopment analysis (DEA) is a nonparametric method in operations research and economics for the estimation of production frontiers. [1] DEA has been applied in a large range of fields including international banking, economic sustainability, police department operations, and logistical applications [2] [3] [4] Additionally, DEA has been used to assess the performance of natural language ...
Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m ≥ n). It is used in some forms of nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations.