# bw.scott

##### Scott's Rule for Bandwidth Selection for Kernel Density

Use Scott's rule of thumb to determine the smoothing bandwidth for the kernel estimation of point process intensity.

##### Usage

`bw.scott(X, isotropic=FALSE, d=NULL)` bw.scott.iso(X)

##### Arguments

- X
A point pattern (object of class

`"ppp"`

,`"lpp"`

,`"pp3"`

or`"ppx"`

).- isotropic
Logical value indicating whether to compute a single bandwidth for an isotropic Gaussian kernel (

`isotropic=TRUE`

) or separate bandwidths for each coordinate axis (`isotropic=FALSE`

, the default).- d
Advanced use only. An integer value that should be used in Scott's formula instead of the true number of spatial dimensions.

##### Details

These functions select a bandwidth `sigma`

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

or `density.lpp`

or other appropriate functions.
They can be applied to a point pattern
belonging to any class `"ppp"`

, `"lpp"`

, `"pp3"`

or `"ppx"`

.

The bandwidth \(\sigma\) is computed by the rule of thumb of Scott (1992, page 152, equation 6.42). The bandwidth is proportional to \(n^{-1/(d+4)}\) where \(n\) is the number of points and \(d\) is the number of spatial dimensions.

This rule is very fast to compute. It typically produces a larger bandwidth
than `bw.diggle`

. It is useful for estimating
gradual trend.

If `isotropic=FALSE`

(the default), `bw.scott`

provides a
separate bandwidth for each coordinate axis, and the result of the
function is a vector, of length equal to the number of coordinates.
If `isotropic=TRUE`

, a single bandwidth value is computed
and the result is a single numeric value.

`bw.scott.iso(X)`

is equivalent to
`bw.scott(X, isotropic=TRUE)`

.

The default value of \(d\) is as follows:

class |
dimension |

`"ppp"` |
2 |

`"lpp"` |
1 |

`"pp3"` |
3 |

The use of `d=1`

for point patterns on a linear network
(class `"lpp"`

) was proposed by McSwiggan et al (2016)
and Rakshit et al (2019).

##### Value

A numerical value giving the selected bandwidth, or a numerical vector giving the selected bandwidths for each coordinate.

##### References

Scott, D.W. (1992)
*Multivariate Density Estimation. Theory, Practice and
Visualization*.
New York: Wiley.

McSwiggan, G., Baddeley, A. and Nair, G. (2016)
Kernel density estimation on a linear network.
*Scandinavian Journal of Statistics* **44** (2) 324--345.

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*.
In press.

##### See Also

##### Examples

```
# NOT RUN {
hickory <- split(lansing)[["hickory"]]
b <- bw.scott(hickory)
b
# }
# NOT RUN {
plot(density(hickory, b))
# }
# NOT RUN {
bw.scott.iso(hickory)
bw.scott(chicago)
bw.scott(osteo$pts[[1]])
# }
```

*Documentation reproduced from package spatstat, version 1.63-0, License: GPL (>= 2)*