bw.scott | R Documentation |
Use Scott's rule of thumb to determine the smoothing bandwidth for the kernel estimation of point process intensity.
bw.scott(X, isotropic=FALSE, d=NULL)
bw.scott.iso(X)
X |
A point pattern (object of class |
isotropic |
Logical value indicating whether to compute a single
bandwidth for an isotropic Gaussian kernel ( |
d |
Advanced use only. An integer value that should be used in Scott's formula instead of the true number of spatial dimensions. |
These functions select a bandwidth sigma
for the kernel estimator of point process intensity
computed by density.ppp
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 |
"ppx" | number of spatial coordinates |
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).
A numerical value giving the selected bandwidth, or a numerical vector giving the selected bandwidths for each coordinate.
.
Scott, D.W. (1992) Multivariate Density Estimation. Theory, Practice and Visualization. New York: Wiley.
density.ppp
,
bw.diggle
,
bw.ppl
,
bw.CvL
,
bw.frac
.
hickory <- split(lansing)[["hickory"]]
b <- bw.scott(hickory)
b
if(interactive()) {
plot(density(hickory, b))
}
bw.scott.iso(hickory)
bw.scott(osteo$pts[[1]])
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