R: Likelihood Cross Validation Bandwidth Selection for Kernel...

bw.ppl {spatstat.core} | R Documentation

## Likelihood Cross Validation Bandwidth Selection for Kernel Density

### Description

Uses likelihood cross-validation to select a smoothing bandwidth for the kernel estimation of point process intensity.

### Usage

       bw.ppl(X, ..., srange=NULL, ns=16, sigma=NULL, weights=NULL,
              shortcut=FALSE, warn=TRUE)

### Arguments

`X` | A point pattern (object of class `"ppp"`).
`srange` | Optional numeric vector of length 2 giving the range of values of bandwidth to be searched.
`ns` | Optional integer giving the number of values of bandwidth to search.
`sigma` | Optional. Vector of values of the bandwidth to be searched. Overrides the values of `ns` and `srange`.
`weights` | Optional. Numeric vector of weights for the points of `X`. Argument passed to `density.ppp`.
`...` | Additional arguments passed to `density.ppp`.
`shortcut` | Logical value indicating whether to speed up the calculation by omitting the integral term in the cross-validation criterion.
`warn` | Logical. If `TRUE`, issue a warning if the maximum of the cross-validation criterion occurs at one of the ends of the search interval.

### Details

This function selects an appropriate bandwidth `sigma` for the kernel estimator of point process intensity computed by `density.ppp`.

The bandwidth σ is chosen to maximise the point process likelihood cross-validation criterion

LCV(σ) = sum[i] log(λ[-i](x[i])) - integral[W] λ(u) du

where the sum is taken over all the data points x[i], where λ[-i](x_i) is the leave-one-out kernel-smoothing estimate of the intensity at x[i] with smoothing bandwidth σ, and λ(u) is the kernel-smoothing estimate of the intensity at a spatial location u with smoothing bandwidth σ. See Loader(1999, Section 5.3).

The value of LCV(σ) is computed directly, using `density.ppp`, for `ns` different values of σ between `srange[1]` and `srange[2]`.

The result is a numerical value giving the selected bandwidth. The result also belongs to the class `"bw.optim"` which can be plotted to show the (rescaled) mean-square error as a function of `sigma`.

If `shortcut=TRUE`, the computation is accelerated by omitting the integral term in the equation above. This is valid because the integral is approximately constant.

### Value

A numerical value giving the selected bandwidth. The result also belongs to the class `"bw.optim"` which can be plotted.

### Author(s)

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

### References

Loader, C. (1999) Local Regression and Likelihood. Springer, New York.

### See Also

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

### Examples

      if(interactive()) {
        b <- bw.ppl(redwood)
        plot(b, main="Likelihood cross validation for redwoods")
        plot(density(redwood, b))
      }

[Package spatstat.core version 2.3-0 Index]