The local pivotal method (LPM) utilizing auxiliary data in sample selection has recently been proposed as a sampling method for national forest inventories (NFIs). Its performance compared to simple random sampling (SRS) and LPM with geographical coordinates has produced promising results in simulation studies. In this simulation study we compared all these sampling methods to systematic sampling. The LPM samples were selected solely using the coordinates (LPMxy) or, in addition to that, auxiliary remote sensing-based forest variables (RS variables). We utilized field measurement data (NFI-field) and Multi-Source NFI (MS-NFI) maps as target data, and independent MS-NFI maps as auxiliary data. The designs were compared using relative efficiency (RE); a ratio of mean squared errors of the reference sampling design against the studied design. Applying a method in NFI also requires a proven estimator for the variance. Therefore, three different variance estimators were evaluated against the empirical variance of replications: 1) an estimator corresponding to SRS; 2) a Grafström-Schelin estimator repurposed for LPM; and 3) a Matérn estimator applied in the Finnish NFI for systematic sampling design. The LPMxy was nearly comparable with the systematic design for the most target variables. The REs of the LPM designs utilizing auxiliary data compared to the systematic design varied between 0.74–1.18, according to the studied target variable. The SRS estimator for variance was expectedly the most biased and conservative estimator. Similarly, the Grafström-Schelin estimator gave overestimates in the case of LPMxy. When the RS variables were utilized as auxiliary data, the Grafström-Schelin estimates tended to underestimate the empirical variance. In systematic sampling the Matérn and Grafström-Schelin estimators performed for practical purposes equally. LPM optimized for a specific variable tended to be more efficient than systematic sampling, but all of the considered LPM designs were less efficient than the systematic sampling design for some target variables. The Grafström-Schelin estimator could be used as such with LPMxy or instead of the Matérn estimator in systematic sampling. Further studies of the variance estimators are needed if other auxiliary variables are to be used in LPM.

中文翻译：

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国家森林资源清查的局部关键方法和系统抽样比较

最近提出了在样本选择中利用辅助数据的局部关键方法（LPM）作为国家森林清单（NFI）的抽样方法。与简单随机抽样（SRS）和具有地理坐标的LPM相比，其性能在模拟研究中产生了可喜的结果。在此模拟研究中，我们将所有这些采样方法与系统采样进行了比较。仅使用坐标（LPMxy）或另外基于辅助遥感的森林变量（RS变量）选择LPM样本。我们将现场测量数据（NFI-field）和多源NFI（MS-NFI）图用作目标数据，将独立的MS-NFI图用作辅助数据。使用相对效率（RE）比较设计；参考抽样设计与研究设计的均方误差之比。在NFI中应用方法还需要经过验证的估计方差。因此，针对复制的经验方差评估了三种不同的方差估计量：1）对应于SRS的估计量；2）重新用于LPM的Grafström-Schelin估计器；3）在芬兰NFI中采用的Matérn估算器进行系统抽样设计。LPMxy与大多数目标变量的系统设计几乎可比。根据研究的目标变量，与系统设计相比，使用辅助数据的LPM设计的RE在0.74至1.18之间变化。期望方差的SRS估计量是最有偏见和最保守的估计量。同样，在LPMxy的情况下，Grafström-Schelin估计器也高估了。当RS变量用作辅助数据时，Grafström-Schelin估计往往低估了经验方差。在系统采样中，Matérn和Grafström-Schelin估计量在实际应用中均表现良好。针对特定变量优化的LPM往往比系统采样更有效率，但是对于某些目标变量，所有考虑的LPM设计都比系统采样设计效率低。Grafström-Schelin估计器可以与LPMxy一起使用，或者在系统采样中代替Matérn估计器。如果要在LPM中使用其他辅助变量，则需要对方差估计量进行进一步研究。针对特定变量优化的LPM往往比系统采样更有效率，但是对于某些目标变量，所有考虑的LPM设计都比系统采样设计效率低。Grafström-Schelin估计器可以与LPMxy一起使用，或者在系统采样中代替Matérn估计器。如果要在LPM中使用其他辅助变量，则需要对方差估计量进行进一步研究。针对特定变量优化的LPM往往比系统采样更有效率，但是对于某些目标变量，所有考虑的LPM设计都比系统采样设计效率低。Grafström-Schelin估计器可以与LPMxy一起使用，或者在系统采样中代替Matérn估计器。如果要在LPM中使用其他辅助变量，则需要对方差估计量进行进一步研究。