# densityQuick.lpp

##### Kernel Estimation of Intensity on a Network using a 2D Kernel

Estimates the intensity of a point process on a linear network using a two-dimensional smoothing kernel.

- Keywords
- spatial, nonparametric

##### Usage

```
densityQuick.lpp(X, sigma=NULL, …,
kernel="gaussian",
at = c("pixels", "points"),
what = c("estimate", "se", "var"),
leaveoneout = TRUE,
diggle = FALSE,
edge2D = FALSE,
weights = NULL,
positive = FALSE)
```

##### Arguments

- X
Point pattern on a linear network (object of class

`"lpp"`

).- sigma
Smoothing bandwidth. A single numeric value, in the same units as the coordinates of

`X`

. Alternatively`sigma`

may be a function which selects a bandwidth when applied to`X`

, for example,`bw.scott.iso`

.- …
Additional arguments passed to

`as.mask`

to determine the pixel resolution.- kernel
String (partially matched) specifying the smoothing kernel. Current options are

`"gaussian"`

,`"epanechnikov"`

,`"quartic"`

or`"disc"`

.- at
String (partially matched) specifying whether to compute the intensity values at a grid of pixel locations (

`at="pixels"`

) or only at the points of`x`

(`at="points"`

).- what
String (partially matched) specifying whether to calculate the intensity estimate, or its estimated standard error, or its estimated variance.

- leaveoneout
Logical value indicating whether to compute a leave-one-out estimator. Applicable only when

`at="points"`

.- diggle
Logical value specifying whether to use the ‘Diggle’ correction.

- edge2D
Logical value specifying whether to apply the usual two-dimensional edge correction procedure to the numerator and denominator of the estimate.

- weights
Optional weights to be attached to the points. A numeric vector, an

`expression`

, or a pixel image.- positive
Logical value indicating whether to force the resulting values to be positive. Default is

`FALSE`

for the sake of speed.

##### Details

Kernel smoothing is applied to the points of `x`

using a two-dimensional Gaussian kernel, as described in Rakshit et al (2019).
The result is a pixel image on the linear network (class
`"linim"`

) which can be plotted.

Other techniques for kernel smoothing on a network are implemented in
`density.lpp`

. The main advantages of using a
two-dimensional kernel are very fast computation and
insensitivity to changes in the network geometry. The main
disadvantage is that it ignores the connectivity of the network.
See Rakshit et al (2019) for further explanation.

##### Value

Image on a linear network (object of class `"linim"`

).

##### Infinite bandwidth

If `sigma=Inf`

, the resulting density estimate is
constant over all locations,
and is equal to the average density of points per unit length.
(If the network is not connected, then this rule
is applied separately to each connected component of the network).

##### References

Rakshit, S., Davies, T., Moradi, M.,
McSwiggan, G., Nair, G., Mateu, J. and Baddeley, A. (2019)
Fast kernel smoothing of point patterns on a large
network using 2D convolution.
*International Statistical Review* **87** (3) 531--556.
DOI: 10.1111/insr.12327.

##### See Also

`density.lpp`

, the main function for density estimation
on a network.

`bw.scott`

, `bw.scott.iso`

for bandwidth selection.

##### Examples

```
# NOT RUN {
X <- unmark(chicago)
plot(densityQuick.lpp(X, 500))
plot(densityQuick.lpp(X, 500, diggle=TRUE))
plot(densityQuick.lpp(X, bw.scott.iso))
plot(densityQuick.lpp(X, 500, what="se"))
# }
```

*Documentation reproduced from package spatstat, version 1.64-1, License: GPL (>= 2)*