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

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bw.stoyanR Documentation

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.


bw.stoyan(X, co=0.15)



A point pattern (object of class "ppp").


Coefficient appearing in the rule of thumb. See 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.


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



and \rolf


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



spatstat.explore documentation built on May 29, 2024, 4:04 a.m.