Multivariate kernel density estimation: Difference between revisions

Revision as of 16:19, 15 September 2010

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== Implementation in the R statistical software ==

The [http://cran.r-project.org/web/packages/ks/index.html ks package]<ref>{{cite journal | author1=Duong, T. | title=ks: Kernel density estimation and kernel discriminant analysis in R | journal=Journal of Statistical Software | year=2007 | volume=21(7) | url=http://www.jstatsoft.org/v21/i07}}</ref> in the [[R programming language]] implements the plug-in and smoothed cross validation selectors. This example is based on the [[Old Faithful Geyser]] in Yellowstone National Park, USA. This dataset contains

272 records with two measurements each: the eruption duration time (minutes) and the

waiting time until the next eruption (minutes), and is contained in the base distribution of R.

This code snippet computes the kernel density estimate with the plug-in bandwidth matrix. The coloured contours correspond to the smallest region which contains that corresponding probability mass: red = 25%, orange + red = 50%, yellow + orange + red = 75%. To compute the SCV selector, replace <code>Hpi</code> with <code>Hscv</code>. This is not displayed here since it is mostly similar to the plug-in estimate.

[[Image:Old Faithful Geyser KDE with plugin bandwidth.png|thumb]]

This code snippet computes the kernel density estimate with the plug-in bandwidth matrix. The coloured contours correspond to the smallest region which contains that corresponding probability mass: red = 25%, orange + red = 50%, yellow + orange + red = 75%. To compute the SCV selector, replace <code>Hpi</code> with <code>Hscv</code>.

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[[Image:Old Faithful Geyser KDE with plugin bandwidth.png|thumbcenter|360px]]

== References ==

<!--- See http://en.wikipedia.org/wiki/Wikipedia:Footnotes on how to create references using <ref></ref> tags which will then appear here automatically -->

{{Reflist}}

== External links ==

* [http://www.mvstat.net/tduong/research www.mvstat.net/tduong/research] Web page containing the mathematical details of multivariate kernel density estimation and their bandwidth selectors.

* [http://www.example.com/ example.com]

==See also==

<!--- Categories --->

*[[Kernel density estimation]] Univariate kernel density estimation.

[[Category:Articles created via the Article Wizard]]

*[[Kernel smoothing]] Univariate kernel regression.

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