Kdhat(X, r = NULL, ReferenceType, NeighborType = ReferenceType, Weighted = FALSE, Original = TRUE, Approximate = ifelse(X$n < 10000, 0, 1), Adjust = 1, MaxRange = "ThirdW", StartFromMinR = FALSE, CheckArguments = TRUE)wmppp.object) or a Dtable object.
NULL, a default value is set: 512 equally spaced values are used, from the smallest distance between points to half the diameter of the window.
NeighborType is ignored then) to estimate the average value of simulated Kd values under the null hypothesis of RandomLocation (Marcon and Puech, 2012).
TRUE, estimates the Kemp function.
TRUE (by default), the original bandwidth selection by Duranton and Overman (2005) following Silverman (1986: 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.
Original) to be multiplied by Adjust. Setting it to values lower than one (1/2 for example) will sharpen the estimation.
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, distances are smoothed down to $r=0$.
Ignored if Approximate is not 0: then, estimation always starts from $r=0$.
TRUE, the function arguments are verified. Should be set to FALSE to save time in simulations for example, when the arguments have been checked elsewhere.
r are those of the density function). The kernel estimator is Gaussian.
The weighted Kd function has been named Kemp (emp is for employees) by Duranton and Overman (2005).
If X is not a Dtable object, the maximum value of r is obtained from the geometry of the window rather than caculating the median distance between points as suggested by Duranton and Overman (2005) to save (a lot of) calculation time.
Sheather, S. J. and Jones, M. C. (1991) A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society series B, 53, 683-690. Silverman, B. W. (1986). Density estimation for statistics and data analysis. Chapman and Hall, London.
KdEnvelope, Mhat
data(paracou16)
plot(paracou16)
# Calculate Kd
(Paracou <- Kdhat(paracou16, , "Q. Rosea", "V. Americana"))
# Plot
plot(Paracou)
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