# Nonparametric Statistical Model

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A Nonparametric Statistical Model is a Statistical Model that requires few assumptions about the underlying Dataset.

**AKA:**Nonparametric Statistics, Distribution Free Method.**Context:**- It can be used by a Nonparametric Statistical Model Algorithm.

**Example(s):****Counter-Example(s):****See:**Generative Model, Kernel Density Estimation Algorithm, Gaussian Process Algorithm.

## References

### 2016

- (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/Non-parametric_statistics#Non-parametric_models
*Non-parametric models*differ from parametric models in that the model structure is not specified*a priori*but is instead determined from data. The term*non-parametric*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 coefficients similar to those obtained by multivariate analysis without any distributional assumption.
- KNNs classify the unseen instance based on the K points in the training set which are nearest to it.
- A support vector machine (with a Gaussian kernel) is a nonparametric large-margin classifier.
- Non-parametrics models can be extended to artificial neural networks

### 2009

- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Non-parametric_statistics
- In Statistics, the term
**non-parametric 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 non-parametric statistical models, inference and statistical tests.*non-parametric 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 non-parametric approaches.*non-parametric regression*refers to modelling where the structure of the relationship between variables is treated non-parametrically, but where nevertheless there may be parametric assumptions about the distribution of model residuals.

- In Statistics, the term

### 2009

- Zoubin Ghahramani. (2009). http://learning.eng.cam.ac.uk/zoubin/nonparam.html
- Non-parametric models are very flexible statistical models in which the complexity of the model grows with the amount of observed data. While traditional parametric models make strong assumptions about how the data was generated, non-parametric models try to make weaker assumptions and let the data "speak for itself". Many non-parametric models can be seen as infinite limits of finite parametric models, and an important family of non-parametric models are derived from Dirichlet processes. See also Gaussian Processes.

### 2006

- (Wasserman, 2006) ⇒ Larry Wasserman. (2006). “All of Nonparametric Statistics." Springer.
- QUOTE: What is Nonparametric Inference?