KdEnvelope(X, r = NULL, NumberOfSimulations = 100, Alpha = 0.05, ReferenceType, NeighborType = ReferenceType, Weighted = FALSE, Original = TRUE, Approximate = ifelse(X$n < 10000, 0, 1), Adjust = 1, MaxRange = "ThirdW", StartFromMinR = FALSE, SimulationType = "RandomLocation", Global = FALSE)wmppp.object) or a Dtable object.
NULL, a default value is set: 512 equally spaced values are used, and the first 256 are returned, corresponding to half the maximum distance between points (following Duranton and Overman, 2005).
TRUE, estimates the Kemp function.
TRUE (by default), the original bandwidth selection by Duranton and Overman (2005) following Silverman (2006: eq 3.31) is used. If FALSE, it is calculated following Sheather and Jones (1991), i.e. the state of the art. See bw.SJ for more details.
Approximate single values equally spaced between 0 and the largest distance. This technique (Scholl and Brenner, 2015) allows saving a lot of memory when addressing large point sets (the default value is 1 over 10000 points). Increasing Approximate allows better precision at the cost of proportional memory use. Ignored if X is a Dtable object.
Adjust. Setting it to values lower than one (1/2 for example) will sharpen the estimation. If not 1, Original is ignored.
r to consider, ignored if r is not NULL. Default is "ThirdW", one third of the diameter of the window. Other choices are "HalfW", and "QuarterW" and "D02005".
"HalfW", and "QuarterW" are for half or the quarter of the diameter of the window.
"D02005" is for the median distance observed between points, following Duranton and Overman (2005). "ThirdW" should be close to "DO2005" but has the advantage to be independent of the point types chosen as ReferenceType and NeighborType, to simplify comparisons between different types. "D02005" is approximated by "ThirdW" if Approximate is not 0.
if X is a Dtable object, the diameter of the window is taken as the max distance between points.
TRUE, points are assumed to be further from each other than the minimum observed distance, So Kd will not be estimated below it: it is assumed to be 0. If FALSE, by default, distances are smoothed down to $r=0$.
Ignored if Approximate is not 0: then, estimation always starts from $r=0$.
TRUE, a global envelope sensu Duranton and Overman (2005) is calculated.
envelope). There are methods for print and plot for this class.The fv contains the observed value of the function, its average simulated value and the confidence envelope.
Scholl, T. and Brenner, T. (2015) Optimizing distance-based methods for large data sets, Journal of Geographical Systems 17(4): 333-351.
Silverman, B. W. (1986). Density estimation for statistics and data analysis. Chapman and Hall, London.
Kdhat
data(paracou16)
plot(paracou16[paracou16$marks$PointType=="Q. Rosea"])
# Calculate confidence envelope
plot(KdEnvelope(paracou16, , ReferenceType="Q. Rosea", Global=TRUE))
# Center of the confidence interval
Kdhat(paracou16, ReferenceType="") -> kd
lines(kd$Kd ~ kd$r, lty=3, col="green")
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