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. 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. 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.

中文翻译：

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有系统抽样的森林资源清单方差估计量的比较-人工种群的结果

大面积森林清单通常使用采样位置的规则网格（以一个随机开始的方式），以确保在被调查种群的整个空间内采样强度均匀。此设计不存在设计无偏差的估计量。通常，使用适用于简单随机抽样（SRS）的准默认估算器，即使该估算器带有以实际重要的余量高估方差的可能风险。为了更好地利用系统抽样的准确性，我们评估了五个方差估计量的性能，其中包括准违约。在这项研究中，模拟的系统抽样应用于具有相反协方差结构且有或没有线性趋势的人工种群。我们将获得的结果与SRS，Matérn的，连续差异复制，Ripley的，和D'Orazio的方差估算器。用SRS方差估计量的四个替代方法获得的方差高度相关，并且在所有研究设置中，与SRS估计量相比，在所有研究设置中始终更接近目标设计方差。后者总是产生最大的高估。在空间自相关几乎为零的总体中，所有估计量均表现均等，并提供接近实际设计方差的估计量。如果没有线性趋势，则SDR和DOR估计值最佳，方差估计值在基准范围内分布更窄。然而，就平均绝对偏差最小而言，马特恩的估算者仍然领先。具有强烈或中等的线性趋势，可以选择Matérn的估算器。在人口众多且采样强度较低的情况下，