spatstat.explore (version 3.3-1)

bw.smoothppp: Cross Validated Bandwidth Selection for Spatial Smoothing

Description

Uses least-squares cross-validation to select a smoothing bandwidth for spatial smoothing of marks.

Usage

bw.smoothppp(X, nh = spatstat.options("n.bandwidth"),
                hmin=NULL, hmax=NULL, warn=TRUE, kernel="gaussian",
                varcov1=NULL)

Value

A single numerical value giving the selected bandwidth. The result also belongs to the class "bw.optim"

(see bw.optim.object) which can be plotted to show the bandwidth selection criterion as a function of sigma.

Arguments

X

A marked point pattern with numeric marks.

nh

Number of trial values of smoothing bandwith sigma to consider. The default is 32.

hmin, hmax

Optional. Numeric values. Range of trial values of smoothing bandwith sigma to consider. There is a sensible default.

warn

Logical. If TRUE, issue a warning if the minimum of the cross-validation criterion occurs at one of the ends of the search interval.

kernel

The smoothing kernel. A character string specifying the smoothing kernel (current options are "gaussian", "epanechnikov", "quartic" or "disc").

varcov1

Optional. Variance-covariance matrix matrix of the kernel with bandwidth \(h=1\). See section on Anisotropic Smoothing.

Anisotropic Smoothing

Anisotropic smoothing is available in Smooth.ppp using the argument varcov to specify the variance-covariance matrix of the anisotropic kernel. In order to choose the matrix varcov, the user can call bw.smoothppp using the argument varcov1 to specify a ‘template’ matrix. Scalar multiples of varcov1 will be considered and the optimal scale factor will be determined. That is, bw.smoothppp will try smoothing the data using varcov = h^2 * varcov1 for different values of h ranging from hmin to hmax. The result of bw.smoothppp will be the optimal value of the standard deviation scale factor h.

Author

Adrian Baddeley and Rolf Turner

Details

This function selects an appropriate bandwidth for the nonparametric smoothing of mark values using Smooth.ppp.

The argument X must be a marked point pattern with a vector or data frame of marks. All mark values must be numeric.

The bandwidth is selected by least-squares cross-validation. Let \(y_i\) be the mark value at the \(i\)th data point. For a particular choice of smoothing bandwidth, let \(\hat y_i\) be the smoothed value at the \(i\)th data point. Then the bandwidth is chosen to minimise the squared error of the smoothed values \(\sum_i (y_i - \hat y_i)^2\).

The result of bw.smoothppp is a numerical value giving the selected bandwidth sigma. The result also belongs to the class "bw.optim" allowing it to be printed and plotted. The plot shows the cross-validation criterion as a function of bandwidth.

The range of values for the smoothing bandwidth sigma is set by the arguments hmin, hmax. There is a sensible default, based on the nearest neighbour distances.

If the optimal bandwidth is achieved at an endpoint of the interval [hmin, hmax], the algorithm will issue a warning (unless warn=FALSE). If this occurs, then it is probably advisable to expand the interval by changing the arguments hmin, hmax.

Computation time depends on the number nh of trial values considered, and also on the range [hmin, hmax] of values considered, because larger values of sigma require calculations involving more pairs of data points.

See Also

Smooth.ppp, bw.optim.object

Examples

  op <- spatstat.options(n.bandwidth=8)
  b <- bw.smoothppp(longleaf)
  b
  plot(b)
  spatstat.options(op)