LISTAhat {stpp}

Estimation of the Space-Time Inhomogeneous Pair Correlation LISTA functions

Description

Compute an estimate of the space-time pair correlarion LISTA functions.

Usage

LISTAhat(xyt, s.region, t.region, dist, times, lambda,
ks = "box", hs, kt = "box", ht, correction = "isotropic")

Arguments

xyt

Coordinates and times (x,y,t) of the point pattern.

s.region

Two-column matrix specifying polygonal region containing all data locations. If s.region is missing, the bounding box of xyt[,1:2] 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.

dist

Vector of distances u at which g^{(i)}(u,v) is computed. If missing, the maximum of dist is given by \min(S_x,S_y)/4, where S_x and S_y represent the maximum width and height of the bounding box of s.region.

times

Vector of times v at which g^{(i)}(u,v) is computed. If missing, the maximum of times is given by (T_{\max} - T_{\min})/4, where T_{\min} and T_{\max} are the minimum and maximum of the time interval T.

lambda

Vector of values of the space-time intensity function evaluated at the points (x,y,t) in S\times T. If lambda is missing, the estimate of the space-time pair correlation function is computed as for the homogeneous case, i.e. considering (n-1)/|S \times T| as an estimate of the space-time intensity.

ks

Kernel function for the spatial distances. Default is the "box" kernel. Can also be "epanech" for the Epanechnikov kernel or "gaussian" or "biweight".

hs

Bandwidth of the kernel function ks.

kt

Kernel function for the temporal distances. Default is the "box" kernel. Can also be "epanech" for the Epanechnikov kernel or "gaussian" or "biweight".

ht

Bandwidth of the kernel function kt.

correction

A character vector specifying the edge correction(s) to be applied among "isotropic", "border", "modified.border", "translate" and "none" (see PCFhat). The default is "isotropic".

Details

An individual product density LISTA functions g^{(i)}(.,.) should reveal the extent of the contribution of the event (u_i,t_i) to the global estimator of the pair correlation function g(.,.), and may provide a further description of structure in the data (e.g., determining events with similar local structure through dissimilarity measures of the individual LISTA functions), for more details see Siino et al. (2017).

Value

A list containing:

list.LISTA

A list containing the values of the estimation of g^{(i)}(r,t) for each one of n points of the point pattern by matrixs.

listatheo

ndist x ntimes matrix containing theoretical values for a Poisson process.

dist, times

Parameters passed in argument.

kernel

Vector of names and bandwidths of the spatial and temporal kernels.

correction

The name(s) of the edge correction method(s) passed in argument.

Author(s)

Francisco J. Rodriguez-Cortes <[e-mail]>

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.

Siino, M., Rodriguez-Cortes, F. J., Mateu, J. and Adelfio, G. (2017). Testing for local structure in spatio-temporal point pattern data. Environmetrics. DOI: 10.1002/env.2463.

Stoyan, D. and Stoyan, H. (1994). Fractals, random shapes, and point fields: methods of geometrical statistics. Chichester: Wiley.