Comparison of estimators of variance for forest inventories with systematic sampling - results from artificial populations

Abstract

Background: Large 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. Results: The 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. Conclusion: Without 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.

A century of national forest inventories – informing past, present and future decisions

“…NFIs are typically based on approximate systematic grids of sample plots which generally produce conservative (i.e., too large) estimates of uncertainty if design-based estimators assuming simple random sampling (SRS) are used. Magnussen et al (2020) document the 100-year long quest of improving variance estimation in systematic sampling using model-based methods and add previously untested estimators to the set of alternatives to using simple expansion estimators with SRS. Of importance for NFIs, they conclude "In large populations, and a low sampling intensity, the performance of the investigated estimators becomes more similar" (Magnussen et al 2020).…”

“…In the context of the Finnish NFI, Räty et al (2020) found, however, that LPM-sampling could not markedly improve estimates based on systematic sampling when considering several variables of interest as is typical in NFIs. Complementing the study by Magnussen et al (2020), Räty et al (2020) identify a variance estimator originally developed for LPM that is well-suited for systematic sampling.…”

A century of National Forest Inventory in Norway – informing past, present, and future decisions

“…Langsaeter 1932Langsaeter , 1934. Among these was a work on uncertainty estimation in systematic strip sampling (Langsaeter 1926) which contained early descriptions of estimators that are still studied today (Magnussen et al 2020).…”

“…The NFI web interface is available in English and Norwegian and gives access to standard NFI data as well (Breidenbach 2016(Breidenbach -2020. Although alternative options are currently considered (Magnussen et al 2020), conservative variance estimators assuming simple random sampling are utilized in the NFI web interface.…”

Comparison of Variance Estimators for Systematic Environmental Sample Surveys: Considerations for Post-Stratified Estimation

“…[25][26]. However, many studies have demonstrated that such estimators may significantly overestimate the true variance [5,6]. Biased estimators of sampling variance can result in a misallocation of resources, as a larger sample size than is necessary to meet some minimum desired precision may be suggested using an inflated variance estimator.…”