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.

中文翻译：

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系统环境抽样调查的方差估计量比较：分层后估计的考虑因素

在二维系统抽样设计下估计点估计量的抽样方差仍然是一个挑战，在过去的几十年中已经提出了几种替代的方差估计量。在这项工作中，我们比较了 Horvitz-Thompson (HT) 和分层后 (PS) 点估计制度下的六个替代方差估计量。我们从大型、空间平衡的国家森林清单中对大量特定物种的森林属性进行二次抽样，以比较方差估计量。假设简单随机抽样设计的方差估计量在 HT 和 PS 点估计制度下表现出正相对偏差，HT 和 PS 的点估计范围分别在 1.23 到 1.88 和 1.11 到 1.78 之间。替代估计量减少了这种正偏差，相对偏差范围在 1.01 到 1.66 和 0.90 到 1 之间。HT 和 PS 分别为 64。替代估计量通常在 HT 和 PS 下获得改进的效率，相对效率值分别介于 0.68 到 1.28 和 0.68 到 1.39 之间。我们确定了两个估计器作为有希望的替代方案，它们在 HT 和 PS 估计机制下为各种属性提供了对简单随机抽样估计器的明显改进。