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 finite positive numerical value giving the selected bandwidth (the standard deviation of the smoothing kernel).
A point pattern (object of class "ppp").
Coefficient appearing in the rule of thumb. See Details.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner rolfturner@posteo.net
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.
Stoyan, D. and Stoyan, H. (1995) Fractals, random shapes and point fields: methods of geometrical statistics. John Wiley and Sons.
pcf,
bw.relrisk