A Nonparametric Test for Spatial Isotropy Using Subsampling
利用子抽样进行空间各向同性的非参数检验AI 解读 ↓
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利用子抽样进行空间各向同性的非参数检验
- 研究问题
- 研究如何正式检验空间过程的相关结构是否具有各向同性，以补充不同方向半变异函数图形诊断的解释局限。
- 方法与思路
- 作者利用样本变异函数的联合渐近正态性，以子抽样估计渐近协方差，再用子抽样分布或卡方极限计算检验显著性。
- 材料陈述的贡献
- 摘要称该检验不需明确指定过程的边际或联合分布，可处理不规则区域，并覆盖规则采样及特定泊松位置采样。
- 阅读关注点
- 应核对子抽样协方差估计的一致性条件、方向与距离的选取，以及规则采样和泊松位置采样下各自的适用要求。
- 阅读边界
- 仅据版本未注明的索引摘要；不规则采样明确限于所述齐次泊松位置机制，其他采样设计的有效性不能据此判断。
原文摘要
A common requirement for spatial modeling is the development of an appropriate correlation structure. Although the assumption of isotropy is often made for this structure, it is not always appropriate. A conventional practice when checking for isotropy is to informally assess plots of direction-specific sample (semi)variograms. Although a useful diagnostic, these graphical techniques are difficult to assess and open to interpretation. Formal alternatives to graphical diagnostics are valuable, but have been applied to a limited class of models. In this article we propose a formal approach to test for isotropy that is both objective and valid for a wide class of models. This approach, which is based on the asymptotic joint normality of the sample variogram, can be used to compare sample variograms in multiple directions. An L2-consistent subsampling estimator for the asymptotic covariance matrix of the sample variogram is derived and used to construct a test statistic. A subsampling approach and a limiting chi-squared approach are developed to obtain p values of the test. Our testing approach is purely nonparametric in that no explicit knowledge of the marginal or joint distribution of the process is needed. In addition, the shape of the random field can be quite irregular. The results apply to regularly spaced data as well as to irregularly spaced data when the point locations are generated by a homogeneous Poisson process. A data example and simulation experiments demonstrate the efficacy of the approach.