Combining double sampling for stratification and cluster sampling to a three-level sampling design for continuous forest inventories. von Lüpke, N. & Saborowski, J. European Journal of Forest Research, 133(1):89–100, 2014.
Combining double sampling for stratification and cluster sampling to a three-level sampling design for continuous forest inventories [pdf]Pdf  doi  abstract   bibtex   
We extend the well-known double sampling for stratification sampling$\$nscheme by cluster subsampling to a three-level design and present$\$ncorresponding estimators based on the infinite population approach$\$nin the first phase. After stratification of the sample points (phase$\$nI), a second-phase sample is drawn independently among the first-phase$\$npoints within each stratum. On level III, clusters are formed of$\$nthose phase II points and a sample of clusters is finally drawn without$\$nreplacement. We used the forest planning units compartment and subdistrict$\$nas clusters and moreover formed clusters with a heuristic for the$\$nvehicle routing problem. The precision of the new estimator was compared$\$nto that achieved with classical double sampling for stratification$\$nin a case study. The results indicate that the expected increase$\$nin sampling errors caused by clustering cannot be compensated by$\$nthe reduced inventory costs under the conditions given in the case$\$nstudy.

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