Geography Reference
In-Depth Information
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Distance
Figure 7.9
Quartic kernel section.
A
B
Figure 7.10
Points within a moving window with a radius of 25 units.
within the circles given, which represent a moving window with a radius of 25 units)
of a larger point pattern. In both cases, there are eight points.
Using the naïve estimator, both point patterns A and B have the same intensity—the
area of the circle is given by
pt
2
= 3.14159 ¥ 25
2
= 1963.495. Given Equation 7.5, in both
cases the intensity estimate is given by
8
/
1963.495
= 0.004074. Using a kernel estimator,
point pattern A has a greater intensity than point pattern B.
Kernel estimation is now illustrated using the same example. Working through
Equation 7.8, the let -hand side (LHS) of the equation,
3
/
pt
2
, is computed i rst. h e
bandwidth,
t
, is set at 25 units, so
3
/
pt
2
=
3
/
(3.14159
¥
25
2
)
= 0.00152.
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