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.

To ensure the bandwidth is finite, an empty point pattern is treated as if it contained 1 point.

Value

A finite positive 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

pcf, bw.relrisk

Aliases
  • bw.stoyan
Examples
# NOT RUN {
  data(shapley)
  bw.stoyan(shapley)
# }
Documentation reproduced from package spatstat, version 1.59-0, License: GPL (>= 2)

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