R: Cross Validated Bandwidth Selection for Spatial Smoothing

bw.smoothppp {spatstat.core} | R Documentation

## 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")

### 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 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.

### Value

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

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### See Also

`Smooth.ppp`

### Examples

      data(longleaf)

      b <- bw.smoothppp(longleaf)
      b
      plot(b)

[Package spatstat.core version 2.4-4 Index]