Multivariate kernel density estimation: Difference between revisions

Revision as of 13:50, 17 September 2010

Revision as of 13:54, 17 September 2010

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One possible solution to this anchor point placement problem to remove the histogram binning grid completely. In the left figure below, a kernel (represented by the dashed grey lines) is centred at each of the 50 data points above. The result of summing these kernels is given on the right figure, which is a kernel density estimate. The most striking difference between kernel density estimates and histograms is that the former are easier to interpret since they do not contain artifices induced by a binning grid.

The coloured contours correspond to the smallest region which contains thatthe correspondingrespective probability mass: red = 25%, orange + red = 50%, yellow + orange + red = 75%, thus indicating that a single central region contains the highest density.

[[Image:Synthetic data 2D KDE.png|center|500px|alt=Left. Individual kernels. Right. Kernel density estimate.|Left. Individual kernels. Right. Kernel density estimate.]]

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waiting time until the next eruption (minutes) of the [[Old Faithful Geyser]] in Yellowstone National Park, USA.

The code fragment computes the kernel density estimate with the plug-in bandwidth matrix <math>\hat{\bold{H}}_\operatorname{PI} = \begin{bmatrix}0.052 & 0.510 \\ 0.510 & 8.882\end{bmatrix}.</math> Again, the coloured contours correspond to the smallest region which contains thatthe correspondingrespective probability mass: red = 25%, orange + red = 50%, yellow + orange + red = 75%. To compute the SCV selector, <code>Hpi</code> is replaced with <code>Hscv</code>. This is not displayed here since it is mostly similar to the plug-in estimate for this example.

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