Epanechnikov kernel
Topic of Hierarchical clustering and kernel density estimation, part of Statistical learning
Epanechnikov kernel
| Type | Topic |
| Taught in | Hierarchical clustering and kernel density estimation |
| Part | Statistical learning |
The kernel K(u)=\tfrac34(1-u^2) on [-1,1], which has bounded support, so a point contributes nothing beyond a finite radius. It minimises asymptotic mean integrated squared error among kernels, though the bandwidth matters far more than the kernel.
In Hierarchical clustering and kernel density estimation
The Epanechnikov kernel has bounded support, so a sample point contributes nothing beyond a finite radius. The normal kernel is the usual multivariate default, and its support is the whole space. A full matrix H can follow an elliptical cloud. A diagonal H, or a product of separate univariate smoothers, has axis-aligned contours. On a tilted cloud those contours place part of each kernel’s mass off the data. One H everywhere is a further restriction: a cloud whose shape changes from one region to another is smoothed with the same orientation in every region.
Used in
See also
Kernel · Kernel density estimator · Choosing the bandwidth · Single, complete, and average linkage · Hierarchical clustering · Agglomerative and divisive clustering · Properties of the linkages · Divisive clustering