dbmss (version 2.0.3)

Kdhat: Estimation of the Kd function

Description

Estimates the Kd function

Usage

Kdhat(X, r, ReferenceType, NeighborType = ReferenceType, Weighted = FALSE,
       Original = TRUE, CheckArguments = TRUE)

Arguments

X

A point pattern (wmppp.object).

r

A vector of distances. No default value is available.

ReferenceType

One of the point types.

NeighborType

One of the point types. By default, the same as reference type.

Weighted

Logical; if TRUE, estimates the Kemp function.

Original

Logical; if 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 o

CheckArguments

Logical; if 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.

Value

• An object of class fv, see fv.object, which can be plotted directly using plot.fv.

Details

Kd is a density, absolute measure of a point pattern structure. Kd is computed efficiently by building a matrix of distances between point pairs and calculating the density of their distribution. The kernel estimator is Gaussian. The weighted Kd function has been named Kemp (emp is for employees) by Duranton and Overman (2005).

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106. 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.

See Also

KdEnvelope, Mhat

Examples

data(paracou16)
plot(paracou16)

# Calculate Kd
r <- 0:100
(Paracou <- Kdhat(paracou16, r, "Q. Rosea", "V. Americana"))
# Plot
plot(Paracou)