Combining double sampling for stratification and cluster sampling to a three-level sampling design for continuous forest inventories

We extend the well-known double sampling for stratification sampling scheme by cluster subsampling to a three-level design and present corresponding estimators based on the infinite population approach in the first phase. After stratification of the sample points (phase I), a second-phase sample is drawn independently among the first-phase points within each stratum. On level III, clusters are formed of those phase II points and a sample of clusters is finally drawn without replacement. We used the forest planning units compartment and subdistrict as clusters and moreover formed clusters with a heuristic for the vehicle routing problem. The precision of the new estimator was compared to that achieved with classical double sampling for stratification in a case study. The results indicate that the expected increase in sampling errors caused by clustering cannot be compensated by the reduced inventory costs under the conditions given in the case study.