R: Scott's Rule for Bandwidth Selection for Kernel Density

bw.scott {spatstat.core} | R Documentation

## Scott's Rule for Bandwidth Selection for Kernel Density

### Description

Use Scott's rule of thumb to determine the smoothing bandwidth for the kernel estimation of point process intensity.

### Usage

       bw.scott(X, isotropic=FALSE, d=NULL)

       bw.scott.iso(X)

### Arguments

`X` | A point pattern (object of class `"ppp"`, `"lpp"`, `"pp3"` or `"ppx"`).
`isotropic` | Logical value indicating whether to compute a single bandwidth for an isotropic Gaussian kernel (`isotropic=TRUE`) or separate bandwidths for each coordinate axis (`isotropic=FALSE`, the default).
`d` | Advanced use only. An integer value that should be used in Scott's formula instead of the true number of spatial dimensions.

### Details

These functions select a bandwidth `sigma` for the kernel estimator of point process intensity computed by `density.ppp` or other appropriate functions. They can be applied to a point pattern belonging to any class `"ppp"`, `"lpp"`, `"pp3"` or `"ppx"`.

The bandwidth σ is computed by the rule of thumb of Scott (1992, page 152, equation 6.42). The bandwidth is proportional to n^(-1/(d+4)) where n is the number of points and d is the number of spatial dimensions.

This rule is very fast to compute. It typically produces a larger bandwidth than `bw.diggle`. It is useful for estimating gradual trend.

If `isotropic=FALSE` (the default), `bw.scott` provides a separate bandwidth for each coordinate axis, and the result of the function is a vector, of length equal to the number of coordinates. If `isotropic=TRUE`, a single bandwidth value is computed and the result is a single numeric value.

`bw.scott.iso(X)` is equivalent to `bw.scott(X, isotropic=TRUE)`.

The default value of d is as follows:

class | dimension
`"ppp"` | 2
`"lpp"` | 1
`"pp3"` | 3
`"ppx"` | number of spatial coordinates

The use of `d=1` for point patterns on a linear network (class `"lpp"`) was proposed by McSwiggan et al (2016) and Rakshit et al (2019).

### Value

A numerical value giving the selected bandwidth, or a numerical vector giving the selected bandwidths for each coordinate.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

### References

Scott, D.W. (1992) Multivariate Density Estimation. Theory, Practice and Visualization. New York: Wiley.

### See Also

`density.ppp`, `bw.diggle`, `bw.ppl`, `bw.CvL`, `bw.frac`.

### Examples

      hickory <- split(lansing)[["hickory"]]
      b <- bw.scott(hickory)
      b
      if(interactive()) {
       plot(density(hickory, b))
      }
      bw.scott.iso(hickory)
      bw.scott(osteo$pts[[1]])

[Package spatstat.core version 1.65-5 Index]