Canadian Forest Service Publications
Design-consistent model-based variances with systematic sampling: a case study with the Danish national Forest inventory. 2019. Magnussen, S., Nord-Larsen, T. Communications in Statistics - Simulation and Computation.
Available from: Pacific Forestry Centre
Catalog ID: 39538
CFS Availability: PDF (request by e-mail)
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To gauge, whether variances in density estimates computed under an assumption of a simple random sampling (SRS) are inflated – when the actual design ensures a spatial balance, we obtained design-consistent, model-based estimators from simulations with replicate samples and anticipated data. Anticipated data is the sum of model-based predictions and a random residual error. Two designs are employed, they bracket the actual design in terms of plot size and number of replicate samples. Results indicate that SRS estimates of uncertainty in ratios of totals have underestimated precision by 30% whereas precision in model-assisted ratios of totals was underestimated by 14%.
Plain Language Summary
Most national forest inventories employs a form of systematic sampling that ensures a geographically balanced sample. Estimates of uncertainty are typically been forwarded under an assumption of a simple random sampling. This can lead to a conservative estimate of uncertainty and confidence intervals that are too wide. The degree of variance inflation can be gauged if the inventory affords the production of a wall-to-wall forest resource map. The forest resource map is then used to simulate all possible design-based systematic samples. The simulated sample data are generated from model-based predictions plus random model-errors. The latter were generated in accordance to the distribution of observed sample fit residuals. In a case study with the Danish National Forest Inventory (2012-2016) we found that the assumption of simple random sampling has probably inflated the estimates of uncertainty by approximately 30%.
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