Year-end Sale % OFF 
Abstract
BackgroundLarge area forest inventories often use regular grids (with a single random start) of sample locations to ensure a uniform sampling intensity across the space of the surveyed populations. A design-unbiased estimator of variance does not exist for this design. Oftentimes, a quasi-default estimator applicable to simple random sampling (SRS) is used, even if it carries with it the likely risk of overestimating the variance by a practically important margin. To better exploit the precision of systematic sampling we assess the performance of five estimators of variance, including the quasi default. In this study, simulated systematic sampling was applied to artificial populations with contrasting covariance structures and with or without linear trends. We compared the results obtained with the SRS, Matérn’s, successive difference replication, Ripley’s, and D’Orazio’s variance estimators.ResultsThe variances obtained with the four alternatives to the SRS estimator of variance were strongly correlated, and in all study settings consistently closer to the target design variance than the estimator for SRS. The latter always produced the greatest overestimation. In populations with a near zero spatial autocorrelation, all estimators, performed equally, and delivered estimates close to the actual design variance.ConclusionWithout a linear trend, the SDR and DOR estimators were best with variance estimates more narrowly distributed around the benchmark; yet in terms of the least average absolute deviation, Matérn’s estimator held a narrow lead. With a strong or moderate linear trend, Matérn’s estimator is choice. In large populations, and a low sampling intensity, the performance of the investigated estimators becomes more similar.
Highlights
Forest inventories have a long history of using systematic sampling (Spurr 1952, p 379) that continues to this date at both local, regional, and national levels (Brooks and Wiant Jr 2004; Kangas and Maltamo 2006; Nelson et al 2008; Tomppo et al 2010; Vidal et al 2016)
Our primary focus is on systematic sampling designs with small populations, and higher than practiced sampling intensities, we demonstrate that a ranking of the relative performances of estimators will be preserved in larger populations and a lower sampling intensity
The correlation between simple random sampling (SRS) and RIP estimates deteriorated to values around − 0.2, but remained around − 0.6 with MAT, successive difference replication estimator of variance (SDR), and DOR for sample sizes ≤900
Summary
Forest inventories have a long history of using systematic sampling (Spurr 1952, p 379) that continues to this date at both local, regional, and national levels (Brooks and Wiant Jr 2004; Kangas and Maltamo 2006; Nelson et al 2008; Tomppo et al 2010; Vidal et al 2016). The bias in the variance estimator for SRS when applied to data from a single systematic sample was recognized early on in Scandinavian countries by Lindeberg (1924), Langsæter (1926), and Näslund (1930), and in North America by Osborne (1942), and Hasel (1942). Langsæter, and Näslund proposed new estimators of variance that generated more realistic estimates of variance for line-transect surveys (Ibid.). Variations of these estimators were later credited to others Oftentimes, a quasi-default estimator applicable to simple random sampling (SRS) is used, even if it carries with it the likely risk of overestimating the variance by a practically important margin. We compared the results obtained with the SRS, Matérn’s, successive difference replication, Ripley’s, and D’Orazio’s variance estimators
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
