kernstadapt (version 0.4.0)

dens.direct: Direct estimation of non-separable adaptive spatio-temporal intensity estimator

Description

Provides an adaptive-bandwidth kernel estimate for spatio-temporal point patterns in a non-separable fashion by calculating the classical estimator, i.e., the slowest estimation.

Usage

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

Value

If at = "points" (the default), 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, with h0 given by OS.

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 non-separable spatio-temporal adaptive kernel estimate of the intensity. It starts from a planar point pattern X and a vector of times t and apply a non-separable kernel estimator for each of the points of X. 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.

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(lGCpp)
X <- lGCpp[sample.int(200)] # A random subset
stIntensity <- dens.direct(X, dimyx = 16, dimt = 4)
plot(spatstat.geom::as.solist(stIntensity), ncols = 4,
     main = 'Non-separable direct example', equal.ribbon = TRUE)

# \donttest{
data(aegiss)
X <- aegiss[sample.int(500)] # A random subset
stIntensity <- dens.direct(X,
                           dimyx = 32, dimt = 16,
                           at = "bins")
plot(spatstat.geom::as.imlist(stIntensity[12:15]),
     main = 'Non-separable direct example')
# }