lambdahat {spatialkernel} | R Documentation |
Kernel density estimation of the intensity function of a two-dimensional point process.
lambdahat(pts, h, gpts = NULL, poly = NULL, edge = TRUE)
pts |
matrix containing the x,y -coordinates of the
data point locations. |
h |
numeric value of the bandwidth used in the kernel smoothing. |
gpts |
matrix containing the x,y -coordinates of point
locations at which to calculate the intensity function, usually
a fine grid points within poly , default NULL to
estimate intensity function at data locations. |
poly |
matrix containing the x,y -coordinates of the
vertices of the polygon boundary in an anticlockwise order. |
edge |
logical, with default TRUE to do edge-correction. |
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 pts, gpts, h, poly, edge . |
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 itemize {