GEOSTATISTICAL ESTIMATION VARIANCE FOR THE SPATIAL MEAN IN TWO-DIMENSIONAL SYSTEMATIC SAMPLING
GEOSTATISTICAL ESTIMATION VARIANCE FOR THE SPATIAL MEAN IN TWO-DIMENSIONAL SYSTEMATIC SAMPLING
复制标题
二维系统采样空间均值的地统计方差估计
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
D. Debouzie
中科院分区：
文献类型：
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作者：
Philippe Aubry;D. Debouzie
许多生态学家使用二维系统抽样来估计采样域上个体的平均密度。他们通常计算均值的方差，就像样本是一个简单的随机样本一样，使用这种抽样设计下的无偏估计量，即o 2/n。这种做法导致选择偏差，即，样本中总体单位的不正确包含概率用于均值方差的估计。偏差的大小随潜在的空间自相关结构而变化。基于设计的推理和基于模型的推理是处理系统样本均值方差估计的两个概念框架。本文报告使用地质统计学估计方差cr2与基于模型的方法。总体空间均值的方差取决于数据的空间自相关结构。我们通过考虑在一个季节期间落在无柄橡树下的橡子的密度来说明该方法。在0.25 m2的正方形样方中对橡子进行编号;数据集是exhaustive。我们从整个样方种群中抽取了9个单起点系统样本。我们计算了整个群体和每个样本的半变异函数，并将其拟合到没有块金的指数模型。利用地统计学的理论结果，我们计算了一个方差的橡子的平均密度的Monte Carlo积分。我们表明，我们的方差估计取决于（1）系统样本的起源，中心样本是最准确的，（2）样方大小，随着样方大小的增加，方差减小，（3）半变异函数模型，（4）离散化的域在蒙特卡洛积分，（5）随机数发生器。考虑到所有的变异来源，在我们的例子中，我们计算的方差估计值范围从-2到36，总平均值等于95个橡子/样方。地统计方差主要反映了样方的位置和大小，以及空间自相关函数。
Many ecologists use two-dimensional systematic sampling to estimate mean density of individuals over the domain sampled. They usually calculate the variance of the mean as if the sample were a simple random sample, using the unbiased estimator under this sampling design, that is, o2/n. This practice leads to a selection bias, i.e., incorrect inclusion probabilities of population units in the sample are used in the estimator of variance of the mean. The magnitude of the bias varies with the underlying spatial autocorrelation structure. Design-based inference and model-based inference are two conceptual frameworks for tackling estimation of variance of the mean in a systematic sample. This paper reports use of the geostatistical estimation variance cr2 with the model-based approach. This variance of the overall spatial mean depends on the spatial autocorrelation structure of the data. We illustrate the method by considering the density of acorns fallen under a sessile oak during one season. Acorns were numbered in square quadrats of 0.25 m2; the data set was ex- haustive. We drew nine one-start systematic samples from the whole population of quadrats. We computed semivariograms for the whole population and each sample and fitted them to exponential models without nugget. Using geostatistical theoretical results, we calculated a variance of the mean density of acorns by Monte Carlo integration. We show that our variance estimate depends on (1) the origin of the systematic sample, the central sample being the most accurate, (2) quadrat size, with a decrease in the variance when quadrat size increases, (3) the semivariogram model, (4) discretization of the domain used in Monte Carlo integration, and (5) the random number generator. Considering all sources of variation, the variance estimate we calculated ranged from -2 to 36 in our example, for an overall mean equal to 95 acorns per quadrat. Geostatistical variance mainly reflects the locations and size of the sampled quadrats, and the spatial autocorrelation function.