Testing for Spatial Isotropy Under General Designs.
Testing for Spatial Isotropy Under General Designs.
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DOI：
10.1016/j.jspi.2011.11.013
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发表时间：
2012-05
影响因子：
0.9
通讯作者：
Sherman M
中科院分区：
文献类型：
--
作者：
Maity A;Sherman M
空间建模通常由均值函数的规范和相关结构的模型组成。关于空间相关性的一个常见假设是它是各向同性的。这意味着，任何两个观测之间的相关性只取决于这些地点之间的距离，而不是它们的相对方位。各向同性的假设通常是因为对相关行为的更简单的解释，以及在假设的各向同性下更容易的估计问题。然而，各向同性假设在不恰当的情况下可能会产生严重的有害影响。本文给出了按一般随机设计定位的空间观测的各向同性检验。推导了检验统计量的分布理论，并进行了大量的模拟实验，验证了该方法的有效性。我们将我们的方法应用于美国南部一片古老森林中的长叶松树的数据集。
Spatial modeling is typically composed of a specification of a mean function and a model for the correlation structure. A common assumption on the spatial correlation is that it is isotropic. This means that the correlation between any two observations depends only on the distance between those sites and not on their relative orientation. The assumption of isotropy is often made due to a simpler interpretation of correlation behavior and to an easier estimation problem under an assumed isotropy. The assumption of isotropy, however, can have serious deleterious effects when not appropriate. In this paper we formulate a test of isotropy for spatial observations located according to a general class of stochastic designs. Distribution theory of our test statistic is derived and we carry out extensive simulations which verify the efficacy of our approach. We apply our methodology to a data set on longleaf pine trees from an oldgrowth forest in the southern United States.