| inhom.thomas.asympcov(InhomCluster) | R Documentation |
Asymptotic covariance matrix for regression parameters in an inhomogeneous Thomas process on a rectangular region S.
inhom.thomas.asympcov=function(z,beta,srule,grule,neighbhd,kappa,omega)
z |
n x (p+1) matrix of covariate values at n spatial locations corresponding to the quadrature points in srule below (first column should consist of ones) |
beta |
p+1 dimensional regression parameter vector in log linear expression for intensity function of inhomogeneous Thomas process |
srule |
quadrature rule for numerical integration over the spatial region S. A list with components x, y and w (area of cell associated with (x,y)), see also details below |
grule |
quadrature rule for numerical integration over a spatial region S_G containing S, see details below. A list with components x, y and w (area of cell associated with (x,y)) |
neighbhd |
Gaussian kernel is truncated to be zero for distances larger than neigbhd. Using neighbdh=4 omega yields a good approximation to the untruncated Gaussian kernel |
kappa |
intensity for `mother' points |
omega |
standard deviation of Gaussian kernel |
The function computes the asymptotic covariance matrix for regression parameters in an inhomogeneous Thomas processes on a rectangular region S, see Waagepetersen (2006). The inhomogeneous Thomas process is obtained by multiplying a log linear term to the random intensity function of a homogeneous Thomas process and the regression parameter estimates are obtained using the score of a Poisson likelihood function as an estimating function.
The quadrature rule srule is for computing numerically integrals over S - see the integrals J and H in Section 3.1 in Waagepetersen (2006). The x and y components in srule should correspond to coordinates of a regular grid covering S and arranged row-wise so that the y coordinate changes quickest. The quadrature rule grule is for computing numerically the integral G where R^2 is replaced by a suitable large region S_G containing S. If S is [a,b] times [c,d] one may take S_G = [a-ext,b + ext] times [c-ext,c+ext] where ext is greater than 4 omega.
A list with components asycov and asycovpois containing asymptotic covariance matrices under either the inhomogeneous Thomas process or the Poisson process with the same intensity function as the inhomogeneous Thomas process.
Rasmus Waagepetersen rw@math.aau.dk http://www.math.aau.dk/~rw
Waagepetersen, R. (2006) An estimation function approach to inference for inhomogeneous Neyman-Scott processes, submitted.