Covariance matrix for the difference between two K-functions

Calculate the covariance matrix for the difference between two K-functions. Also return the contribution to the variance for each of the two point patterns,

khvc(pts1, pts2, poly, s)

Arguments

pts1

An object containing the case locations.

pts2

An object containing the control locations.

poly

A polygon enclosing the locations in pts1 and pts2

s

A vector of distances at which the calculation is to be made.

Value

A list with four components:

varmat

The upper triangle of the covariance matrix.

k11

The variance of Khat for the cases

k22

The variance of Khat for the controls

k12

The covariance of Khat for the cases and Khat for controls.

Note

Note that the diagonal of the covariance matrix is $k11 - 2 * $k12 + $k22

See also

khat, khvmat, secal

References

Rowlingson, B. and Diggle, P. 1993 Splancs: spatial point pattern analysis code in S-Plus. Computers and Geosciences, 19, 627-655; the original sources can be accessed at: https://www.maths.lancs.ac.uk/~rowlings/Splancs/. See also Bivand, R. and Gebhardt, A. 2000 Implementing functions for spatial statistical analysis using the R language. Journal of Geographical Systems, 2, 307-317.