bw.lppl | R Documentation |

Uses likelihood cross-validation to select a smoothing bandwidth for the kernel estimation of point process intensity on a linear network.

bw.lppl(X, ..., srange=NULL, ns=16, sigma=NULL, weights=NULL, distance=c("euclidean", "path"), shortcut=TRUE, warn=TRUE)

`X` |
A point pattern on a linear network (object of class |

`srange` |
Optional numeric vector of length 2 giving the range of values of bandwidth to be searched. |

`ns` |
Optional integer giving the number of values of bandwidth to search. |

`sigma` |
Optional. Vector of values of the bandwidth to be searched.
Overrides the values of |

`weights` |
Optional. Numeric vector of weights for the points of |

`distance` |
Argument passed to |

`...` |
Additional arguments passed to |

`shortcut` |
Logical value indicating whether to speed up the calculation by omitting the integral term in the cross-validation criterion. |

`warn` |
Logical. If |

This function selects an appropriate bandwidth `sigma`

for the kernel estimator of point process intensity
computed by `density.lpp`

.

The argument `X`

should be a point pattern on a linear network
(class `"lpp"`

).

The bandwidth *σ* is chosen to
maximise the point process likelihood cross-validation criterion

*
LCV(σ) = sum[i] log(λ[-i](x[i])) - integral[L] λ(u) du
*

where the sum is taken over all the data points *x[i]*,
where *λ[-i](x_i)* is the
leave-one-out kernel-smoothing estimate of the intensity at
*x[i]* with smoothing bandwidth *σ*,
and *λ(u)* is the kernel-smoothing estimate
of the intensity at a spatial location *u* with smoothing
bandwidth *σ*.
See Loader(1999, Section 5.3).

The value of *LCV(σ)* is computed
directly, using `density.lpp`

,
for `ns`

different values of *σ*
between `srange[1]`

and `srange[2]`

.

The result is a numerical value giving the selected bandwidth.
The result also belongs to the class `"bw.optim"`

which can be plotted to show the (rescaled) mean-square error
as a function of `sigma`

.

If `shortcut=TRUE`

, the computation is accelerated by
omitting the integral term in the equation above. This is valid
because the integral is approximately constant.

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

which can be plotted.

Greg McSwiggan, Suman Rakshit and \adrian.

Loader, C. (1999)
*Local Regression and Likelihood*.
Springer, New York.

McSwiggan, G., Baddeley, A. and Nair, G. (2019)
Estimation of relative risk for events on a linear network.
*Statistics and Computing* **30** (2) 469–484.

`density.lpp`

,
`bw.scott`

.

For point patterns in two-dimensional space, use `bw.ppl`

.

if(interactive()) { b <- bw.lppl(spiders) plot(b, main="Likelihood cross validation for spiders") plot(density(spiders, b, distance="e")) } else { b1 <- bw.lppl(spiders, ns=2) b2 <- bw.lppl(spiders, ns=2, shortcut=TRUE) }

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