Description Usage Arguments Details Value Author(s) References Examples
Computes i-th edge-corrected kernel estimator of the product density LISTA function.
1 2 |
xyt |
Spatial-temporal coordinates (x,y,t) of the point pattern. |
i |
Point position for which you want to calculate a LISTA function. |
s.region |
A two-column matrix specifying a polygonal region containing all data locations. If |
t.region |
vector containing the minimum and maximum values of the time interval. If |
ds |
A vector of distances |
dt |
A vector of distances |
ks |
A kernel function for the spatial distances. The default is |
hs |
A bandwidth of the kernel function |
kt |
A kernel function for the temporal distances. The default is |
ht |
A bandwidth of the kernel function |
correction |
It is |
An individual product density LISTA functions ρ^{(2)i}(.,.) is a puntual contribution coming from (u_i,t_i) to the global estimator of the second-order product density ρ^{(2)}(.,.), and may provide local description of structure in the spatio-temporal point data (e.g., determining events with similar local structure through dissimilarity measures of the individual LISTA functions), for more details see Cressie and Collins (2001).
A list containing:
hlista
: A matrix containing the values of the estimation of \widehat{ρ}^{(2)i}(r,t) for the point i of the process by rows.
ds
: Vector of distances u
at which ρ^{(2)i}(r,t) is computed under the restriction 0<ε<r.
dt
: Vector of distances v
at which ρ^{(2)i}(r,t) is computed under the restriction 0<δ<t.
kernel
: A vector of names and bandwidth of the spatial and temporal kernel.
Francisco J. Rodriguez-Cortes <cortesf@uji.es> https://fjrodriguezcortes.wordpress.com
Baddeley, A. and Turner, J. (2005). spatstat
: An R Package for Analyzing Spatial Point Pattens. Journal of Statistical Software 12, 1-42.
Cressie, N. and Collins, L. B. (2001). Analysis of spatial point patterns using bundles of product density LISA functions. Journal of Agricultural, Biological, and Environmental Statistics 6, 118-135.
Cressie, N. and Collins, L. B. (2001). Patterns in spatial point locations: Local indicators of spatial association in a minefield with clutter Naval Research Logistics (NRL), John Wiley & Sons, Inc. 48, 333-347.
Stoyan, D. and Stoyan, H. (1994). Fractals, random shapes, and point fields: methods of geometrical statistics. Chichester: Wiley.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ## Not run:
#################
# Realisations of the homogeneous spatio-temporal Poisson processes
stp <- rpp(100)$xyt
# Generated spatio-temporal point pattern
plot(stp)
# Randomly selected point and its product density LISTA
fixed <-sample(1:length(stp[,1]),1)
# Estimation of the individual i-th product density LISTA function
out <- iLISTA(stp,i=fixed)
z1 <- out$hlista
# Spatio-temporal LISTA surface
par(mfrow=c(1,1))
persp(out$ds,out$dt,z1,theta=-45,phi=30,zlim=range(z1,na.rm=TRUE),expand=0.7,ticktype="detailed",xlab="r = distance",ylab="t = time",zlab="",cex.axis=0.7, cex.lab=0.7)
contour(out$ds,out$dt,z1,drawlabels=TRUE,axes=TRUE,xlab="r = distance",ylab="t = time",cex.axis=0.7, cex.lab=0.7)
## End(Not run)
#################
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