### Nearest-tree and Variable Polygon Sampling

#### Abstract

Sampling a nearest neighbor is often presented as a Hansen-Hurwitz or Horvitz-Thompson

estimation process. This may not be the most informative viewpoint, and measuring the probability of

selection is not necessary. The measurement of the nearest object as a “depth” over the selection area can

be done by a sampling process, and the total estimated without knowing the polygon areas. The process is

unbiased, quite general, and easy to understand. It can be extended to more than just the nearest object

to a sample point and to many different polygon shapes. This paper is an extension, simplification and

generalization of an earlier paper in this journal (Iles, K. 2009. “Nearest-tree” estimations—A discussion

of their geometry, MCFNS 1(2), pp. 47–51.), but does not require a random orientation or weighting for

the direction of measurement from the tree to the polygon border.

#### Keywords

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PDF#### References

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