Compute an estimate of the space-time pair correlarion LISTA functions.
LISTAhat(xyt, s.region, t.region, dist, times, lambda,
ks = "box", hs, kt = "box", ht, correction = "isotropic")A list containing:
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.
ndist x ntimes matrix containing theoretical values for a Poisson process.
Parameters passed in argument.
Vector of names and bandwidths of the spatial and temporal kernels.
The name(s) of the edge correction method(s) passed in argument.
Coordinates and times \((x,y,t)\) of the point pattern.
Two-column matrix specifying polygonal region containing all data locations. If s.region is missing, the bounding box of xyt[,1:2] is considered.
Vector containing the minimum and maximum values of the time interval. If t.region is missing, the range of xyt[,3] is considered.
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.
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 \(T\).
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.
Kernel function for the spatial distances. Default is the "box" kernel. Can also be "epanech" for the Epanechnikov kernel or "gaussian" or "biweight".
Bandwidth of the kernel function ks.
Kernel function for the temporal distances. Default is the "box" kernel. Can also be "epanech" for the Epanechnikov kernel or "gaussian" or "biweight".
Bandwidth of the kernel function kt.
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".
Francisco J. Rodriguez-Cortes <frrodriguezc@unal.edu.co>
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).
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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.
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