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

Abstract

The estimation of the sampling variance of point estimators under two-dimensional systematic sampling designs remains a challenge, and several alternative variance estimators have been proposed in the past few decades. In this work, we compared six alternative variance estimators under Horvitz-Thompson (HT) and post-stratification (PS) point estimation regimes. We subsampled a multitude of species-specific forest attributes from a large, spatially balanced national forest inventory to compare the variance estimators. A variance estimator that assumes a simple random sampling design exhibited positive relative bias under both HT and PS point estimation regimes ranging between 1.23 to 1.88 and 1.11 to 1.78 for HT and PS, respectively. Alternative estimators reduced this positive bias with relative biases ranging between 1.01 to 1.66 and 0.90 to 1.64 for HT and PS, respectively. The alternative estimators generally obtained improved efficiencies under both HT and PS, with relative efficiency values ranging between 0.68 to 1.28 and 0.68 to 1.39, respectively. We identified two estimators as promising alternatives that provide clear improvements over the simple random sampling estimator for a wide variety of attributes and under HT and PS estimation regimes.

Forests at the fringe: Comparing observed change to projected climate change impacts for five tree species in the Pacific Northwest, United States

“…Therefore, design-based estimators like those in Scott et al (2005) assume simple random sampling within strata and proportional allocation of plots between strata. Recent research has demonstrated that model-based variance estimators can reduce the positive-bias incurred by the simple random sampling assumption of design-based estimators (Frank and Monleon, 2021). However, in this study, we apply the designbased variance estimators of Scott et al (2005) and note that the resulting variance estimates will be conservative.…”

“…When considering estimators for the sample variance of the post-stratified mean, it is important to note that, while the computational burden of design-based estimators is less than that of model-based estimators, a design-based estimator will be conservative for a quasi-systematic sample like the FIA Program's annual inventory (Frank and Monleon, 2021). The conservative nature of these variance estimates will result in a positive-bias and wider confidence intervals than the stated rate (i.e., a "90-percent" CI will have coverage probabilities > 0.9).…”

Estimation of change with partially overlapping and spatially balanced samples

“…Recently, many other studies have been conducted to evaluate different variance estimators in order to find less biased variance estimator of HT estimator using systematic samples, see for example, Babcock et al (2018), Frank and Monleon (2021). For well‐spread samples, we have evaluated our proposed estimators by using and equal inclusion probabilities (representative samples).…”

Comparison of Model-Assisted Endogenous Poststratification Methods for Estimation of Above-Ground Biomass Change in Oregon, USA

“…Nevertheless, the problem is not eliminated, and alternative variance estimators have been proposed to account for spatial correlations when estimating variances from systematic samples [31][32][33]. Recent studies have shown that using these estimators with FIA data can improve the efficiency when estimating variances of spatially correlated attributes, even after post-stratification [34].…”