Bandwidth Selection Based on Window Geometry
Select a smoothing bandwidth for smoothing a point pattern, based only on the geometry of the spatial window. The bandwidth is a specified quantile of the distance between two independent random points in the window.
bw.frac(X, ..., f=1/4)
This function selects an appropriate bandwidth
for the kernel estimator of point process intensity
The bandwidth $\sigma$ is computed as a quantile of the distance between two independent random points in the window. The default is the lower quartile of this distribution.
If $F(r)$ is the cumulative distribution function of the distance between two independent random points uniformly distributed in the window, then the value returned is the quantile with probability $f$. That is, the bandwidth is the value $r$ such that $F(r) = f$.
The cumulative distribution function $F(r)$ is
distcdf. We then
we compute the smallest number $r$
such that $F(r) \ge f$.
- A numerical value giving the selected bandwidth.
The result also belongs to the class
"bw.frac"which can be plotted to show the cumulative distribution function and the selected quantile.
h <- bw.frac(letterR) h plot(h, main="bw.frac(letterR)")