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)
X |
A point pattern (object of class |
co |
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(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.
A finite positive numerical value giving the selected bandwidth (the standard deviation of the smoothing kernel).
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
Stoyan, D. and Stoyan, H. (1995) Fractals, random shapes and point fields: methods of geometrical statistics. John Wiley and Sons.
data(shapley) bw.stoyan(shapley)
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