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).

- X
A point pattern (object of class

`"ppp"`

).- co
Coefficient appearing in the rule of thumb. See Details.

Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner r.turner@auckland.ac.nz

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`