Nearest-tree and Variable Polygon Sampling

Kim Iles


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.


n-tree sampling; nearest tree; Voronoi polygons; unbiased estimates.

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