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An approximate point-based alternative for the estimation of variance under big BAF sampling
Forest Ecosystems ( IF 4.1 ) Pub Date : 2021-05-27 , DOI: 10.1186/s40663-021-00304-0
Thomas B. Lynch , Jeffrey H. Gove , Timothy G. Gregoire , Mark J. Ducey

A new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes Bitterlich sampling (point sampling) with two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation. The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means. The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula. Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature. In simulations the new estimator performed well and comparably to existing variance formulas. A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees, an assumption required by all previous big BAF variance estimation formulas. Although this correlation was negligible on the simulation stands used in this study, it is conceivable that the correlation could be significant in some forest types, such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition. We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area. We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of $\frac {1}{n}$ where n is the number of sample points.

中文翻译:

大BAF采样下基于近似点的方差估计

得出了一个新的方差估计器,并针对大型BAF(基础面积因子)抽样进行了测试,该抽样是一种森林清查系统,该系统使用具有两个BAF大小的Bitterlich抽样(点抽样),用于树计数的小型BAF和用于进行树木测量的较大BAF通常包括DBH和体积估计所需的高度。新的估计量是使用Delta方法从包含三个样本均值的大型BAF估计量的现有公式中得出的。将该新公式与现有的大型BAF估算器进行比较,其中包括基于布鲁斯公式的流行估算器。进行了一些计算机模拟研究,将新的方差估计量与当前森林清单文献中所有大BAF的所有已知方差估计量进行了比较。在仿真中,新的估算器表现良好,与现有方差公式相当。新估计量的可能优势在于,它不需要对小BAF因子上的基础面积计数与基于大BAF因子选择树的体积-基础面积比之间的可忽略的相关性进行假设,而先前所有大BAF都需要进行这种假设方差估计公式。尽管在本研究中使用的模拟林台上这种相关性可以忽略不计,但是可以想象该相关性在某些森林类型中可能是显着的,例如其中DBH-高度关系可能受到密度(可能是通过竞争而受到显着影响)的那些类型。我们推导了一个公式,该公式可用于估计平均基础面积估计值与平均​​体积和平均基础面积估计值之比之间的协方差。我们还通过数学推导得出了大型BAF估计器中的偏差表达式,该表达式可用于显示在大样本中偏差接近零,其顺序为\\ frac {1} {n} $,其中n是样本点的数量。
更新日期:2021-05-27
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