Evaluating the Percentage Points of a Spatial Autocorrelation Coefficient
Evaluating the Percentage Points of a Spatial Autocorrelation Coefficient
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评估空间自相关系数的百分点
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
K. Ord
中科院分区：
文献类型：
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作者：
A. Cliff;K. Ord
在文献中已经提出了各种统计数据来测试在一个“国家”的每个“县”测量的随机变量的空间自相关的存在。这些措施在Cliff和Ord [ I ]中进行了审查。在大多数经验应用中，研究人员希望确定所用检验系数计算值的显著性程度。不幸的是，很少有人知道任何的空间自相关系数的采样分布，特别是在尾部地区的显着性测试是至关重要的，在小型和中型的格子通常会遇到。这显然是一个严重的障碍，在提出一个可靠的检验显着性的任何系数。本文的目的是评估以下定义的空间自相关系数的尾部区域中的抽样分布。一个合适的近似抽样分布的系数建议提供了一个可靠的显着性检验的基础。使用Monte Carlo方法。考虑一个由n个县组成的县系统。假设变量X在n个县中的每一个县都进行了测量。设第i个县的X值为xi，定义xi = xi 2。县i对县j的影响由权重wij表示。然后，作者提出了[ I ]，xi之间的空间自相关的以下度量：
Various statistics have been proposed in the literature to test for the presence of spatial autocorrelation on a random variable measured in each ‘county’ of a ‘country’. These measures are reviewed in Cliff and Ord [ I ] . In most empirical applications, the researcher will wish to determine the degree of significance of the calculated value of the test coefficient used. Unfortunately, very little is known about the sampling distributions of any of the spatial autocorrelation coefficients, particularly in the tail areas which are critical for significance testing, in the small and moderate sized lattices usually encountered. This is clearly a severe handicap in proposing a reliable test of significance for any of the coefficients. It is the purpose of this paper to evaluate the sampling distribution in the tail areas of the spatial autocorrelation coefficient defined below. A suitable approximation to the sampling distribution of the coefficient is suggested which provides the basis for a reliable test of significance. Monte Carlo methods are used. Consider a county system which comprises n counties. Suppose that a variate, X , has been measured in each of the n counties. Let the value of X in the ith county be xi and define x i = xi 2. The effect of county i on county j is denoted by the weight, wij . Then, the authors have proposed [ I ] , the following measure of spatial autocorrelation between the xi :