spatstat (version 1.23-4)

bw.diggle: Cross Validated Bandwidth Selection for Kernel Density

Description

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

Usage

bw.diggle(X)

Arguments

X

A point pattern (object of class "ppp").

Value

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

Details

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

The bandwidth $\sigma$ is chosen to minimise the mean-square error criterion defined by Diggle (1985). The algorithm computes the mean-square error by the method of Berman and Diggle (1989). See Diggle (2003, page 117) for a summary.

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.

References

Berman, M. and Diggle, P. (1989) Estimating weighted integrals of the second-order intensity of a spatial point process. Journal of the Royal Statistical Society, series B 51, 81--92.

Diggle, P.J. (1985) A kernel method for smoothing point process data. Applied Statistics (Journal of the Royal Statistical Society, Series C) 34 (1985) 138--147.

Diggle, P.J. (2003) Statistical analysis of spatial point patterns, Second edition. Arnold.

See Also

density.ppp

Examples

data(lansing)
  attach(split(lansing))
  b <- bw.diggle(hickory)
  plot(b, ylim=c(-2.5, 0), main="Cross validation for hickories")
  plot(density(hickory, b))

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