自空间平均被创立以来,无论是在科研还是在实践中都得到了广泛的应用,并取得了一定的成果｡空间平均中权重系数的估计问题一直是众多学者研究分析的课题｡在缺失数据的情况下,空间平均是关于两个随机变量R=∑βsr以及S=∑βs的比率｡文章假设在权重β已知的情况下,利用“Delta方法”推导了iiiiiiii用于估计真实空间平均的估计量r的平方偏差､方差和均方误差的近似公式,分析了估计量r的偏差以及方差来源,并给出最小化偏差的空间平均估计权重,最后将所得结果运用于全球氨氧化古菌相对丰度数据｡

Spatial averages have been widely used in scientific research and practical applications since they were proposed. How to estimate the weight coefficient in the spatial average has been a problem studied by many scholars. In the case of missing data, the spatial average is the ratio of the two random variables R = ∑ βi si ri as well as S = ∑ βi si . In this paper, we use the “ Delta method”to derive approximate formulas for the squared bias, variance, and mean squared error of the estimatorr used to estimate the true spatial average, assuming that the weight βi is known. The bias of the estimator r and the source of variance are analyzed, and the spatial average estimated weight to minimize the bias is given. Finally, the obtained results are applied to the global relative abundance data of ammoniating archaea.