Description Usage Arguments Details Value Note References See Also
Kernel density estimation of the intensity function of a two-dimensional point process.
1 |
pts |
matrix containing the |
h |
numeric value of the bandwidth used in the kernel smoothing. |
gpts |
matrix containing the |
poly |
matrix containing the |
edge |
logical, with default |
Kernel smoothing methods are widely used to estimate the intensity of a spatial point process. One problem which arises is the need to handle edge effects. Several methods of edge-correction have been proposed. The adjustment factor proposed in Berman and Diggle (1989) is a double integration int_AK[(x-x_0)/h]/h^2, where A is a polygonal area, K is the smoothing kernel and h is the bandwidth used for the smoothing. Zheng, P. et\ al (2004) proposed an algorithm for fast calculate of Berman and Diggle's adjustment factor.
When gpts
is NULL
, lambdahat
uses a
leave-one-out estimator for the intensity at each of the
data points, as been suggested in Baddeley et al
(2000). This leave-one-out estimate at each of the data points
then can be used in the inhomogeneous K function estimation
kinhat
when the true intensity function is unknown.
The default kernel is the Gaussian.
The kernel function is selected by calling setkernel
.
A list with components
lambda |
numeric vector of the estimated intensity function. |
... |
copy of the arguments |
In principle, the double adaptive double integration algorithm of Zheng, P. et\ al (2004) can be applied to other kernel functions.
Other source codes used in the implementation of the double integration algorithm include
Laurie, D.P. (1982) adaptive cubature code in Fortran;
Shewchuk, J.R. triangulation code in C;
Alan Murta's polygon intersection code in C (Project: Generic Polygon Clipper).
M. Berman and P. Diggle (1989) Estimating weighted integrals of the second-order intensity of a spatial point process, J. R. Stat. Soc. B, 51, 81–92.
P. Zheng, P.A. Durr and P.J. Diggle (2004) Edge–correction for Spatial Kernel Smoothing — When Is It Necessary? Proceedings of the GisVet Conference 2004, University of Guelph, Ontario, Canada, June 2004.
Baddeley, A. J. and M<f8>ller, J. and Waagepetersen R. (2000) Non and semi-parametric estimation of interaction in inhomogeneous point patterns, Statistica Neerlandica, 54, 3, 329–350.
Laurie, D.P. (1982). Algorithm 584 CUBTRI: Adaptive Cubature over a Triangle. ACM–Trans. Math. Software, 8, 210–218.
Jonathan R. Shewchuk, Triangle, a Two-Dimensional Quality Mesh Generator and Delaunay Triangulator at http://www-2.cs.cmu.edu/~quake/triangle.html.
Alan Murta, General Polygon Clipper at http://www.cs.man.ac.uk/~toby/gpc.
NAG's Numerical Library. Chapter 11: Quadrature, NAG's Fortran 90 Library. (http://www.nag.co.uk/numeric/fn/manual/html/c11_fn03.html)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.