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Fixed numbers in MISE eval

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Markus Bullmann
2018-05-08 11:52:08 +02:00
parent 9f358d69c9
commit 23b8f0886e
3 changed files with 5 additions and 5 deletions
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6
tex/chapters/experiments.tex
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@@ -27,7 +27,7 @@ Four estimates are computed with varying bandwidth using the KDE, BKDE, BoxKDE,
All estimates are calculated at $30\times 30$ equally spaced points.
%Evaluated at $50^2$ points the exact KDE is compared to the BKDE, BoxKDE, and extended box filter approximation, which are evaluated at a smaller grid with $30^2$ points.
The graphs of the MISE between $f$ and the estimates as a function of $h\in[0.15, 1.0]$ are given in \figref{fig:errorBandwidth}.
A minimum error is obtained with $h=0.35$, for larger values oversmoothing occurs and the modes gradually fuse together.
A minimum error is obtained with $h=0.25$, for larger values oversmoothing occurs and the modes gradually fuse together.
Both the BKDE and the ExBoxKDE resemble the error curve of the KDE quite well and stable.
They are rather close to each other, with a tendency to diverge for larger $h$.
@@ -36,8 +36,8 @@ These jumps are caused by the rounding of the integer-valued box width given by
As the extended box filter is able to approximate an exact $\sigma$, such discontinuities do not appear.
Consequently, it reduces the overall error of the approximation, even though only marginal in this scenario.
The global average MISE over all values of $h$ is $0.0049$ for the regular box filter and $0.0047$ in case of the extended version.
Likewise, the maximum MISE is $0.0093$ and $0.0091$, respectively.
The global average MISE over all values of $h$ is $0.0051$ for the regular box filter and $0.0049$ in case of the extended version.
The global maximum MISE is $0.0011$ for both versions.
The choice between the extended and regular box filter algorithm depends on how large the acceptable error should be, thus on the particular application.
Other test cases of theoretical relevance are the MISE as a function of the grid size $G$ and the sample size $N$.