CONSTRUCTING A NEIGHBOURHOOD

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For a data set with sample size n=21 and span size w=0.25, there are [wn]=5 points in each window. The neighbourhood, Ni, of the point i is as follows :

Point Ni
1 1,2,3
2 1,2,3,4
3 1,2,3,4,5
4 2,3,4,5,6
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18 16,17,18,19,20
19 17,18,19,20,21
20 18,19,20,21
21 19,20,21

In this example the neighbourhoods of points 1,2,20 and 21 are truncated.

Neighbourhoods can be calculated by the following formula

formula

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Generalized Additive Models 23.4.96 Page : 7a of 15