Provides fixed bandwidths for spatial or spatiotemporal data based on the maximal smoothing (oversmoothing) principle of Terrell (1990).
1 2 3 4 5 6 7 8 9 10 11 12
An object of class
Optional. Controls the value to use in place of the number of
observations n in the oversmoothing formula. Either a character
Optional. Controls the value for a scalar representation of
the spatial (and temporal for
A numeric vector of equal length to the number of points in
These functions calculate scalar smoothing bandwidths for kernel density
estimates of spatial or spatiotemporal data: the “maximal amount of smoothing
compatible with the estimated scale of the observed data”. See Terrell
OS function returns a single bandwidth for isotropic smoothing
of spatial (2D) data. The
OS.spattemp function returns two values – one for
the spatial margin and another for the temporal margin, based on independently applying
Terrell's (1990) rule (in 2D and 1D) to the spatial and temporal margins of the supplied data.
requires a sample size, and this can be minimally tailored via
By default, the function simply uses the number of observations in
nstar = "npoints". Alternatively, the user can specify their own value by simply
supplying a single positive numeric value to
OS (not applicable to
pp is a
ppp.object with factor-valued
marks, then the user has the option of using
nstar = "geometric", which sets the sample size used in the formula
to the geometric mean of the counts of observations of each mark. This can
be useful for e.g. relative risk calculations, see Davies and Hazelton
scaler argument is used to specify spatial
(as well as temporal, in use of
OS.spattemp) scale. For isotropic smoothing in the spatial
margin, one may use the ‘robust’ estimate
of standard deviation found by a weighted mean of the interquartile ranges
of the x- and y-coordinates of the data respectively
scaler = "IQR"). Two other options are the raw mean of the
coordinate-wise standard deviations (
scaler = "sd"), or the square
root of the mean of the two variances (
scaler = "var"). A fourth
scaler = "silverman" (default), sets the scaling constant to
be the minimum of the
"sd" options; see Silverman
(1986), p. 47. In use of
OS.spattemp the univariate version of the elected scale
statistic is applied to the recorded times of the data for the temporal bandwidth.
nstar, the user can specify their
own value by simply supplying a single positive numeric value to
OS, or a numeric vector of length 2 (in the order of [<spatial scale>, <temporal scale>])
A single numeric value of the estimated spatial bandwidth for
OS, or a named numeric vector of length 2 giving
the spatial bandwidth (as
h) and the temporal bandwidth (as
Davies, T.M. and Hazelton, M.L. (2010), Adaptive kernel estimation of spatial relative risk, Statistics in Medicine, 29(23) 2423-2437.
Terrell, G.R. (1990), The maximal smoothing principle in density estimation, Journal of the American Statistical Association, 85, 470-477.
1 2 3 4 5 6 7 8 9
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.