484 Spatial Point Patterns: Methodology and Applications with R
the empirical curve
b
K(r), rather than exactly matching it. In the present co ntext, D is called the con-
trast between the two curves; estimating ψ by minimising D is the method of minimum contrast.
Taking a finely spaced sequence of distances would effectively replace the sum (12.29) by the
integral
D(ψ) =
Z
b
a
(K
ψ
(r) −
b
K(r))
2
dr (12.30)
where a and b are the limits of the range of distances considere d. This measures the separation
between the two curves K
ψ
(r) an d
b
K(r) over the distance inter val [a, b]. The squared error in
(12.29)–(12.30) could be replaced by the absolute error
D(ψ) =
Z
b
a
K
ψ
(r) −
b
K(r)
dr
which is the total area between the two curves. We could also pre-transform the ...