Cross Validated Bandwidth Selection for Spatial Smoothing
Uses least-squares cross-validation to select a smoothing bandwidth for spatial smoothing of marks.
bw.smoothppp(X, nh = spatstat.options("n.bandwidth"),
hmin=NULL, hmax=NULL, warn=TRUE, kernel="gaussian")X |
A marked point pattern with numeric marks. |
nh |
Number of trial values of smoothing bandwith |
hmin, hmax |
Optional. Numeric values.
Range of trial values of smoothing bandwith |
warn |
Logical. If |
kernel |
The smoothing kernel.
A character string specifying the smoothing kernel
(current options are |
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 ith data point. For a particular choice of smoothing bandwidth, let y*[i] be the smoothed value at the ith data point. Then the bandwidth is chosen to minimise the squared error of the smoothed values sum (y[i] - 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.
A numerical value giving the selected bandwidth.
The result also belongs to the class "bw.optim"
which can be plotted.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
data(longleaf) b <- bw.smoothppp(longleaf) b plot(b)
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