Computes a rough estimate of the appropriate bandwidth for kernel smoothing estimators of the pair correlation function and other quantities.
A point pattern (object of class
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
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
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
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).
Stoyan, D. and Stoyan, H. (1995) Fractals, random shapes and point fields: methods of geometrical statistics. John Wiley and Sons.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.