Multivariate kernel density estimation: Difference between revisions

Revision as of 06:27, 14 August 2015

Revision as of 06:32, 14 August 2015

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</source>

==Density estimation in R with a diagonal bandwidth matrix==

[[File:Old faithful pdf.png|thumb|250px|alt=Old Faithful Geyser data kernel density estimate with diagonal bandwidth matrix.|Old Faithful Geyser data kernel density estimate with diagonal bandwidth matrix.]]

==Density estimation with a diagonal bandwidth matrix==

This example is again based on the Old Faithful Geyser, but this time we use the [http://cran.r-project.org/web/packages/np/index.html R np package] that employs automatic (data-driven) bandwidth selection for a diagonal bandwidth matrix; see the [http://cran.r-project.org/web/packages/np/vignettes/np.pdf np vignette] for an introduction to the np package. The figure below shows the joint density estimate using a second order Gaussian kernel.

'''R script for the example'''

The following commands of the R programming language use the

{{mono|npudens()}} function to deliver optimal smoothing and to create

the figure given above. These commands can be entered at the command

prompt by using copy and paste.

<source lang="rsplus" style="overflow:auto;">

library(np)

library(datasets)

data(faithful)

f <- npudens(~eruptions+waiting,data=faithful)

plot(f,view="fixed",neval=100,phi=30,main="",xtrim=-0.2)

</source>

Computing kernel density estimates with diagonal bandwidth selectors is also available in the {{mono|ks}} library, using the {{mono|Hpi.diag()}} function. To produce a 3D plot similar to that from {{mono|npudens()}}, the option {{mono|display="persp"}} is added.

<source lang="rsplus" style="overflow:auto;">

library(ks)

data(faithful)

H <- Hpi.diag(x=faithful)

fhat <- kde(x=faithful, H=H)

plot(fhat, display="persp")

</source>

==Density estimation in Matlab with a diagonal bandwidth matrix==

{{howto|section|date=July 2015}}

[[File:Bivariate example.png|thumb|250px|alt=Kernel density estimate with diagonal bandwidth for synthetic normal mixture data. |Kernel density estimate with diagonal bandwidth for synthetic normal mixture data.]]

Line 164 ⟶ 194:

contour3(X,Y,density,50), hold on

plot(data(:,1),data(:,2),'r.','MarkerSize',5)

</source>

==Density estimation in R with a diagonal bandwidth matrix==

{{howto|section|date=July 2015}}

[[File:Old faithful pdf.png|thumb|250px|alt=Old Faithful Geyser data kernel density estimate with diagonal bandwidth matrix.|Old Faithful Geyser data kernel density estimate with diagonal bandwidth matrix.]]

This example is again based on the Old Faithful Geyser, but this time we use the [http://cran.r-project.org/web/packages/np/index.html R np package] that employs automatic (data-driven) bandwidth selection for a diagonal bandwidth matrix; see the [http://cran.r-project.org/web/packages/np/vignettes/np.pdf np vignette] for an introduction to the np package. The figure below shows the joint density estimate using a second order Gaussian kernel.

'''R script for the example'''

The following commands of the R programming language use the

{{mono|npudens()}} function to deliver optimal smoothing and to create

the figure given above. These commands can be entered at the command

prompt by using copy and paste.

<source lang="rsplus" style="overflow:auto;">

library(np)

library(datasets)

data(faithful)

f <- npudens(~eruptions+waiting,data=faithful)

plot(f,view="fixed",neval=100,phi=30,main="",xtrim=-0.2)

</source>

Computing kernel density estimates with diagonal bandwidth selectors is also available in the {{mono|ks}} library, using the {{mono|Hpi.diag()}} function. To produce a 3D plot similar to that from {{mono|npudens()}}, the option {{mono|display="persp"}} is added.

<source lang="rsplus" style="overflow:auto;">

library(ks)

data(faithful)

H <- Hpi.diag(x=faithful)

fhat <- kde(x=faithful, H=H)

plot(fhat, display="persp")

</source>