Description Usage Arguments Details Value Author(s) See Also Examples

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

1 2 | ```
bw.smoothppp(X, nh = spatstat.options("n.bandwidth"),
hmin=NULL, hmax=NULL, warn=TRUE)
``` |

`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 |

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 *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 (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.

and \rolf

1 2 3 4 5 6 | ```
data(longleaf)
b <- bw.smoothppp(longleaf)
b
plot(b)
``` |

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