SepTest (version 0.0.1)

estimate.intensity.pixel: Kernel-based intensity estimation on a space-time grid and its components, and test statistics for first-order separability

Description

Computes kernel-smoothed estimates of spatial, temporal, separable, and non-separable spatio-temporal intensity functions on a regular space-time grid, together with separability diagnostics used in first-order separability analysis.

Usage

estimate.intensity.pixel(X, s.region, t.region, n.grid, edge, owin = NULL)

Value

A list with grid coordinates x,y,t, intensity estimates, the diagnostic S.fun, its marginal summaries S.space and S.time, and deviation measures.

Arguments

X

Numeric matrix/data.frame with three columns (x, y, t) giving observed events.

s.region

Numeric matrix with two columns defining the spatial window (typically polygon vertices). Grid limits are taken as range(s.region[,1]) and range(s.region[,2]).

t.region

Numeric vector of length 2 giving the temporal window c(tmin, tmax).

n.grid

Integer vector of length 3 giving grid resolution in \(x\), \(y\), and \(t\).

edge

List with components bw (length 3), space (length nrow(X)), and time (length nrow(X)).

owin

Optional observation window of class "owin" (from spatstat.geom). If provided, intensity estimates outside the window are set to NA.

Details

The estimator uses product Gaussian kernels with supplied bandwidths and (Gaussian) edge-correction factors, typically produced by calc.bandwidths.and.edgecorr.

References

Ghorbani, M., Vafaei, N., Dvořák, J., and Myllymäki, M. (2021). Testing the first-order separability hypothesis for spatio-temporal point patterns. Computational Statistics & Data Analysis, 161, 107245.

See Also

S.based.functions, calc.bandwidths.and.edgecorr

Examples

n <- 100
X <- cbind(x = stats::runif(n), y = stats::runif(n), t = stats::runif(n, 0, 10))
s.region <- matrix(c(0,0, 1,0, 1,1, 0,1), ncol=2, byrow=TRUE)
t.region <- c(0, 10)
n.grid <- c(10, 10, 5)
edge <- list(bw = c(0.05, 0.05, 0.5), space = rep(1, n), time = rep(1, n))
res <- estimate.intensity.pixel(X, s.region, t.region, n.grid, edge)
str(res)