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

In spatstat.core: Core Functionality of the 'spatstat' Family

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.

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(λ) where λ 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 σ = 0.15/sqrt(5 * λ).

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).

Author(s)

\adrian

and \rolf

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)

spatstat.core documentation built on May 18, 2022, 9:05 a.m.