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m Correcting two errors: 1) the definition of AMISE contained an extra transpose on vecH, and 2) m_2 comes from the integral of xx^T K(x), not xx^t K(x)^2. Corrections from Wand and Jones reference. |
convert depreciated tt tag. Also fix missing opening/closing tt tag using AWB (10497) |
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The following commands of the R programming language use the
the figure given above. These commands can be entered at the command
prompt by using copy and paste.
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</source>
Computing kernel density estimates with diagonal bandwidth selectors is also available in the
<source lang="rsplus" style="overflow:auto;">
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===Alternative optimality criteria===
The MISE is the expected integrated ''L<sub>2</sub>'' distance between the density estimate and the true density function ''f''. It is the most widely used, mostly due to its tractability and most software implement MISE-based bandwidth selectors.
There are alternative optimality criteria, which attempt to cover cases where MISE is not an appropriate measure.<ref name="simonoff1996"/>{{rp|
: <math>\operatorname{MIAE} (\bold{H}) = \operatorname{E}\, \int |\hat{f}_\bold{H} (\bold{x}) - f(\bold{x})| \, d\bold{x}.</math>
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==External links==
* [http://www.mvstat.net/tduong/research mvstat.net] A collection of peer-reviewed articles of the mathematical details of multivariate kernel density estimation and their bandwidth selectors on an
* [http://libagf.sf.net libagf] A [[C++]] library for multivariate, [[variable bandwidth kernel density estimation]].
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