Nonparametric regression: Difference between revisions

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{{Short description|Category of regression analysis}}

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'''Nonparametric regression''' is a categoryform of [[regression analysis]] in whichwhere the predictor does not take a predetermined form but is completely constructed according tousing information derived from the data. That is, no [[parametric formequation]] is assumed for the relationship between [[Dependent_and_independent_variables|predictors]] and dependent variable. Nonparametric regression requiresA larger [[Sampling_(statistics)|sample]] sizessize thanis regressionneeded basedto onbuild a nonparametric model having the same level of [[Prediction_interval|uncertainty]] as a [[parametric model]]s because the data must supply both the model structure as well asand the modelparameter estimates.

== Definition ==

InNonparametric nonparametricregression assumes the regressionfollowing relationship, wegiven havethe random variables <math>X</math> and <math>Y</math> and assume the following relationship:

:<math>

\mathbb{E}[Y\mid X=x] = m(x),

</math>

where <math>m(x)</math> is some deterministic function. [[Linear regression]] is a restricted case of nonparametric regression where <math>m(x)</math> is assumed to be affinea linear function of the data.

Some authors useSometimes a slightly stronger assumption of additive noise is used:

:<math>

Y = m(X) + U,

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Without the assumption that <math>m</math> belongs to a specific parametric family of functions it is impossible to get an unbiased estimate for <math>m</math>, however most estimators are [[Consistency_(statistics)|consistent]] under suitable conditions.

== List of general-purposeCommon nonparametric regression algorithms ==

This is a non-exhaustive list of non-parametric models for regression.

* nearest neighbors, see [[nearest- neighbor interpolationsmoothing]] and(see also [[k-nearest neighbors algorithm]] )

* [[regression tree|regression trees]]

* [[kernel regression]]

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* [[multivariate adaptive regression splines]]

* [[smoothing spline|smoothing splines]]

* [[Artificial neural network|neural networks]]<ref>{{Cite journal |last=Cherkassky |first=Vladimir |last2=Mulier |first2=Filip |date=1994 |editor-last=Cheeseman |editor-first=P. |editor2-last=Oldford |editor2-first=R. W. |title=Statistical and neural network techniques for nonparametric regression by Vladimir Cherkassky, Filip Mulier |url=https://link.springer.com/chapter/10.1007/978-1-4612-2660-4_39 |journal=Selecting Models from Data |series=Lecture Notes in Statistics |language=en |___location=New York, NY |publisher=Springer |pages=383–392 |doi=10.1007/978-1-4612-2660-4_39 |isbn=978-1-4612-2660-4|url-access=subscription }}</ref>

== Examples ==