# bw.stoyan

0th

Percentile

##### 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.

Keywords
methods, smooth, spatial
##### 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.

pcf, bw.relrisk
data(shapley)
bw.stoyan(shapley)