kernstadapt (version 0.4.0)

dens.direct.sep: Direct separable adaptive spatio-temporal intensity estimator

Description

Provides an adaptive-bandwidth kernel estimate for spatio-temporal point patterns in a separable fashion, i.e., by multiplying spatial and temporal marginals. This estimation is performed by calculating the classical estimator, i.e., the slowest estimation.

Usage

dens.direct.sep(
  X,
  t = NULL,
  dimyx = 128,
  dimt = 128,
  bw.xy = NULL,
  bw.t = NULL,
  at = c("bins", "points")
)

Value

If at = "points", the result is a numeric vector with one entry for each data point in X. if at = "bins" is a list named (by time-point) list of pixel images (im objects) corresponding to the joint spatio-temporal intensity over space at each discretised time bin.

Arguments

X

A spatial point pattern (an object of class ppp) with the spatial coordinates of the observations. It may contain marks representing times.

t

A numeric vector of temporal coordinates with equal length to the number of points in X. This gives the time associated with each spatial point. This argument is not necessary if time marks are provided to the point pattern X.

dimyx

Spatial pixel resolution. The default is 128 for each axes.

dimt

Temporal bin vector dimension. The default is 128.

bw.xy

Numeric vector of spatial smoothing bandwidths for each point in X. By default this is computed using bw.abram.

bw.t

Numeric vector of temporal smoothing bandwidths for each point in t. By default this is computed using bw.abram.temp.

at

String specifying whether to estimate the intensity at a mesh (at = "bins") or only at the points of X (at = "points").

Author

Jonatan A. González

Details

This function computes a spatio-temporal adaptive kernel estimate of the intensity in a separable fashion. It starts from a planar point pattern X and a vector of times t and uses a direct estimator for each dimension, then it multiplies both components and normalises by the number of points to preserve the mass. The arguments bw.xy and bw.t specify the smoothing bandwidth vectors to be applied to each of the points in X and t. They should be a numeric vectors of bandwidths. The method partition the range of bandwidths into intervals, subdividing the points of the pattern X and t into sub-patterns according to the bandwidths, and applying fixed-bandwidth smoothing to each sub-pattern. Specifying ngroups.xy = 1 is the same as fixed-bandwidth smoothing with bandwidth sigma = median(bw.xy) in the spatial case and ngroups.t = 1 is the same as fixed-bandwidth smoothing with bandwidth sigma = median(bw.xy).

References

González J.A. and Moraga P. (2018) An adaptive kernel estimator for the intensity function of spatio-temporal point processes http://arxiv.org/pdf/2208.12026

Examples

data(santander)
X <- santander[sample.int(200)]
stIntensity <- dens.direct.sep(X,
                               dimyx = 32, dimt = 6,
                               at = "bins")
plot(spatstat.geom::as.solist(stIntensity[2:4]),
     main = 'Direct separable example', equal.ribbon = TRUE)