Nonparametric statistics
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In statistics, the term nonparametric statistics covers a range of topics:

 distribution free methods which do not rely on assumptions that the data are drawn from a given probability distribution. As such it is the opposite of parametric statistics. It includes nonparametric statistical models, inference and statistical tests.
 nonparametric statistic can refer to a statistic (a function on a sample) whose interpretation does not depend on the population fitting any parametrized distributions. Statistics cased on the ranks of observations are one example of such statistics and these play a central role in many nonparametric approaches.
 nonparametric regression refers to modelling where the structure of the relationship between variables is treated nonparametrically, but where nevertheless there may be parametric assumptions about the distribution of model residuals.
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[edit] Applications and purpose
Nonparametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars). The use of nonparametric methods may be necessary when data has a ranking but no clear numerical interpretation, such as when assessing preferences; in terms of levels of measurement, for data on an ordinal scale.
As nonparametric methods make fewer assumptions, their applicability is much wider than the corresponding parametric methods. In particular, they may be applied in situations where less is known about the application in question. Also, due to the reliance on fewer assumptions, nonparametric methods are more robust.
Another justification for the use of nonparametric methods is simplicity. In certain cases, even when the use of parametric methods is justified, nonparametric methods may be easier to use. Due both to this simplicity and to their greater robustness, nonparametric methods are seen by some statisticians as leaving less room for improper use and misunderstanding.
The wider applicability and increased robustness of nonparametric tests comes at a cost: in cases where a parametric test would be appropriate, nonparametric tests have less power. In other words, a larger sample size can be required to draw conclusions with the same degree of confidence.
[edit] Nonparametric models
Nonparametric models differ from parametric models in that the model structure is not specified a priori but is instead determined from data. The term nonparametric is not meant to imply that such models completely lack parameters but that the number and nature of the parameters are flexible and not fixed in advance.
 A histogram is a simple nonparametric estimate of a probability distribution
 Kernel density estimation provides better estimates of the density than histograms.
 Nonparametric regression and semiparametric regression methods have been developed based on kernels, splines, and wavelets.
 Data Envelopment Analysis provides efficiency coeficients similar to those obtained by Multivariate Analysis without any distributional assumption.
[edit] Methods
Nonparametric (or distributionfree) inferential statistical methods are mathematical procedures for statistical hypothesis testing which, unlike parametric statistics, make no assumptions about the probability distributions of the variables being assessed. The most frequently used tests include
 AndersonDarling test
 Cochran's Q
 Cohen's kappa
 EfronPetrosian test
 Friedman twoway analysis of variance by ranks
 Kendall's tau
 Kendall's W
 KolmogorovSmirnov test
 KruskalWallis oneway analysis of variance by ranks
 Kuiper's test
 MannWhitney U or Wilcoxon rank sum test
 Maximum parsimony for the development of species relationships using computational phylogenetics
 median test
 Pitman's permutation test
 Rank products
 SiegelTukey test
 Spearman's rank correlation coefficient
 StudentNewmanKeuls (SNK) test
 Van Elteren stratified Wilcoxon Rank Sum Test
 WaldWolfowitz runs test
 Wilcoxon signedrank test.
[edit] General references
 Corder, G.W. & Foreman, D.I, "Nonparametric Statistics for NonStatisticians: A StepbyStep Approach", Wiley (2009) (ISBN: 9780470454619)
 Wasserman, Larry, "All of Nonparametric Statistics", Springer (2007) (ISBN: 0387251456)
 Gibbons, Jean Dickinson and Chakraborti, Subhabrata, "Nonparametric Statistical Inference", 4th Ed. CRC (2003) (ISBN: 0824740521)
[edit] See also
 Parametric statistics
 Resampling (statistics)
 Robust statistics
 Particle filter for the general theory of sequential Monte Carlo methods