bw.smoothppp
Cross Validated Bandwidth Selection for Spatial Smoothing
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")
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"
).
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.
Value
A numerical value giving the selected bandwidth.
The result also belongs to the class "bw.optim"
which can be plotted.
See Also
Examples
# NOT RUN {
data(longleaf)
# }
# NOT RUN {
b <- bw.smoothppp(longleaf)
b
plot(b)
# }