
734 Spatial Point Patterns: Methodology and Applications with R
where
κ
(·) is a smoothing kernel on the real line. Standar d techniques for one-dimensional kernel
smoothing [687] can be u sed.
We call ( 17.10) the geometrica lly corrected function because the de nominator m(x
i
,d
L
(x
i
,x
j
))
adjusts for the geometry of the network . As usual, we nee d to avoid situations where the w e ight
factor m(x
i
,d
L
(x
i
,x
j
)) is zero. It is shown in [19] that the estimator (17.10) is valid f or all r ≤
R, whe re R is the largest value such that m(u,r) 6= 0 for all locations u and all r ≤ R. If L is a
connected networ k, then R = min
u∈L
max
v∈L
d
L
(u,v) is th e radius of ...