Environmental and Ecological Statistics

, Volume 19, Issue 1, pp 107–123

Triangulation based inclusion probabilities: a design-unbiased sampling approach

  • Lutz Fehrmann
  • Timothy G. Gregoire
  • Christoph Kleinn
Open Access

DOI: 10.1007/s10651-011-0177-9

Cite this article as:
Fehrmann, L., Gregoire, T.G. & Kleinn, C. Environ Ecol Stat (2012) 19: 107. doi:10.1007/s10651-011-0177-9


A probabilistic sampling approach for design-unbiased estimation of area-related quantitative characteristics of spatially dispersed population units is proposed. The developed field protocol includes a fixed number of 3 units per sampling location and is based on partial triangulations over their natural neighbors to derive the individual inclusion probabilities. The performance of the proposed design is tested in comparison to fixed area sample plots in a simulation with two forest stands. Evaluation is based on a general approach for areal sampling in which all characteristics of the resulting population of possible samples is derived analytically by means of a complete tessellation of the areal sampling frame. The example simulation shows promising results. Expected errors under this design are comparable to sample plots including a much greater number of trees per plot.


Design based inference Inclusion probability Delaunay Triangulation Plot design Continuous population 
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© The Author(s) 2011

Authors and Affiliations

  • Lutz Fehrmann
    • 1
  • Timothy G. Gregoire
    • 2
  • Christoph Kleinn
    • 1
  1. 1.Chair of Forest Inventory and Remote SensingGeorg-August-Universität GöttingenGöttingenGermany
  2. 2.Yale School of Forestry and Environmental StudiesNew HavenUSA

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