iLISTA: i-th product density LISTA function

Description Usage Arguments Details Value Author(s) References Examples

Description

Computes i-th edge-corrected kernel estimator of the product density LISTA function.

Usage

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iLISTA(xyt, i, s.region, t.region, ds, dt, ks = "epanech", hs,
  kt = "epanech", ht, correction = TRUE)

Arguments

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 s.region is missing, the Ripley-Rasson estimate convex spatial domain is considered.

t.region

vector containing the minimum and maximum values of the time interval. If t.region is missing, the range of xyt[,3] is considered.

ds

A vector of distances u at which ρ^{(2)i}(u,v) is computed.

dt

A vector of distances v at which ρ^{(2)i}(u,v) is computed.

ks

A kernel function for the spatial distances. The default is "epanech" the Epanechnikov kernel. It can also be "box" kernel, or "biweight".

hs

A bandwidth of the kernel function ks.

kt

A kernel function for the temporal distances. The default is "epanech" the Epanechnikov kernel. It can also be "box" kernel, or "biweight".

ht

A bandwidth of the kernel function kt.

correction

It is TRUE by default and the Ripley's isotropic edge-correction weights are computed. If it is FALSE the estimated is without edge-correction.

Details

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).

Value

A list containing:

Author(s)

Francisco J. Rodriguez-Cortes <[email protected]> https://fjrodriguezcortes.wordpress.com

References

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.

Examples

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## 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)
#################

frajaroco/pdLISTA documentation built on May 16, 2019, 1:53 p.m.