# bw.CvL: Cronie and van Lieshout's Criterion for Bandwidth Selection... In spatstat.core: Core Functionality of the 'spatstat' Family

 bw.CvL R Documentation

## Cronie and van Lieshout's Criterion for Bandwidth Selection for Kernel Density

### Description

Uses Cronie and van Lieshout's criterion based on Cambell's formula to select a smoothing bandwidth for the kernel estimation of point process intensity.

### Usage

```   bw.CvL(X, ..., srange = NULL, ns = 16, sigma = NULL, warn=TRUE)
```

### Arguments

 `X` A point pattern (object of class `"ppp"`). `...` Ignored. `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`. `warn` Logical. If `TRUE`, a warning is issued if the optimal value 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 minimise the discrepancy between the area of the observation window and the sum of reciprocal estimated intensity values at the points of the point process

CvL(σ) = (|W| - sum[i] 1/λ(x[i]))^2

where the sum is taken over all the data points x[i], and where λ(x[i]) is the kernel-smoothing estimate of the intensity at x[i] with smoothing bandwidth σ.

The value of CvL(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 bandwidth selection criterion as a function of `sigma`.

### Value

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

### Author(s)

Ottmar Cronie ottmar.cronie@umu.se and Marie-Colette van Lieshout Marie-Colette.van.Lieshout@cwi.nl adapted for spatstat by \spatstatAuthors.

### References

Cronie, O and Van Lieshout, M N M (2018) A non-model-based approach to bandwidth selection for kernel estimators of spatial intensity functions, Biometrika, 105, 455-462.

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

### Examples

```  if(interactive()) {
b <- bw.CvL(redwood)
b
plot(b, main="Cronie and van Lieshout bandwidth criterion for redwoods")
plot(density(redwood, b))
plot(density(redwood, bw.CvL))
}

```

spatstat.core documentation built on May 18, 2022, 9:05 a.m.