Canadian Forest Service Publications

A jackknife estimator of variance for a random tessellated stratified sampling design. 2019. Magnussen, S., Nord-Larsen, T.

Year: 2019

Available from: Pacific Forestry Centre

Catalog ID: 39545

Language: English

CFS Availability: PDF (download)

Available from the Journal's Web site.
DOI: 10.1093/forsci/fxy070

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Abstract

Semisystematic sampling designs—in which a population area frame is tessellated into cells, and a randomly located sample is taken from each cell—affords random tessellated stratified (RTS) Horvitz–Thompson-type estimators. Forest inventory applications with RTS estimators are rare, possibly because of computational complexities with the estimation of variance. To reduce this challenge, we propose a jackknife estimator of variance for RTS designs. We demonstrate an application with a model-assisted ratio of totals estimator and data from the Danish National Forest Inventory. RTS estimators of standard error were, as a rule, smaller than comparable estimates obtained under the assumption of simple random sampling. The proposed jackknife estimator performed well.

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 a false assumption of a simple random sampling (SRS) which leads to conservative estimates of uncertainty. Some national forest inventories employ a semi-systematic design (e.g. the US and Denmark). For these designs random tessellated stratified design estimators (RTS) are appropriate as they provide smaller estimates of variance in presence of a spatial covariance structure. Computations of RTS variances is complex as it involves time-consuming GIS operations on tessellation polygons and nested land-area polygons within them. To reduce the computational burden we propose a jackknife RTS estimator of variance. In an application with the Danish National Forest Inventory, results indicated a good performance of the proposed estimator. The results confirmed that earlier estimators under the SRS assumption were conservative.

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