bw.stoyan
Stoyan's Rule of Thumb for Bandwidth Selection
Computes a rough estimate of the appropriate bandwidth for kernel smoothing estimators of the pair correlation function and other quantities.
Usage
bw.stoyan(X, co=0.15)Arguments
- X
- A point pattern (object of class
"ppp"). - co
- Coefficient appearing in the rule of thumb. See Details.
Details
Estimation of the pair correlation function and other quantities
by smoothing methods requires a choice of the smoothing bandwidth.
Stoyan and Stoyan (1995, equation (15.16), page 285) proposed a
rule of thumb for choosing the smoothing bandwidth.
For the Epanechnikov kernel, the rule of thumb is to set
the kernel's half-width $h$ to
$0.15/\sqrt{\lambda}$ where
$\lambda$ is the estimated intensity of the point pattern,
typically computed as the number of points of X divided by the
area of the window containing X.
For a general kernel, the corresponding rule is to set the
standard deviation of the kernel to
$\sigma = 0.15/\sqrt{5\lambda}$.
The coefficient $0.15$ can be tweaked using the
argument co.
Value
- A numerical value giving the selected bandwidth (the standard deviation of the smoothing kernel).
References
Stoyan, D. and Stoyan, H. (1995) Fractals, random shapes and point fields: methods of geometrical statistics. John Wiley and Sons.
See Also
Examples
data(shapley)
bw.stoyan(shapley)