spatstat (version 1.23-1)

bw.stoyan: Stoyan's Rule of Thumb for Bandwidth Selection

Description

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.

Value

• A numerical value giving the selected bandwidth (the standard deviation of the smoothing kernel).

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.

References

Stoyan, D. and Stoyan, H. (1995) Fractals, random shapes and point fields: methods of geometrical statistics. John Wiley and Sons.

See Also

pcf, bw.relrisk

Examples

data(shapley)
  bw.stoyan(shapley)