ABSTRACT

There are a number of ways to test for the absence/presence of a spatial signal in a completely observed fine-resolution image. One of these is a powerful nonparametric procedure called enhanced false discovery rate (EFDR). A drawback of EFDR is that it requires the data to be defined on regular pixels in a rectangular spatial domain. Here, we develop an EFDR procedure for possibly incomplete data defined on irregular small areas. Motivated by statistical learning, we use conditional simulation (CS) to condition on the available data and simulate the full rectangular image at its finest resolution many times (M, say). EFDR is then applied to each of these simulations resulting in M estimates of the signal and M statistically dependent p-values. Averaging over these estimates yields a single, combined estimate of a possible signal, but inference is needed to determine whether there really is a signal present. We test the original null hypothesis of no signal by combining the $Mp$-values into a single p-value using copulas and a composite likelihood. If the null hypothesis of no signal is rejected, we use the combined estimate. We call this new procedure EFDR-CS and, to demonstrate its effectiveness, we show results from a simulation study; an experiment where we introduce aggregation and incompleteness into temperature-change data in the Asia-Pacific; and an application to total-column carbon dioxide from satellite remote sensing data over a region of the Middle East, Afghanistan, and the western part of Pakistan. Supplementary materials for this article are available online.

摘要

有多种方法可以在完全观察到的高分辨率图像中测试空间信号的缺失/存在。其中之一是强大的非参数程序，称为增强错误发现率 (EFDR)。EFDR 的一个缺点是它需要在矩形空间域中的常规像素上定义数据。在这里，我们为在不规则小区域上定义的可能不完整的数据开发了一个 EFDR 程序。受统计学习的启发，我们使用条件模拟 (CS) 以可用数据为条件，并多次以最高分辨率模拟完整的矩形图像（例如M）。然后将 EFDR 应用于这些模拟中的每一个，从而产生M 个信号估计值和M 个统计相关的p-值。对这些估计求平均会产生对可能信号的单个组合估计，但需要进行推理以确定是否确实存在信号。我们通过结合$米p$-values使用 copulas 和复合似然转换为单个p值。如果拒绝无信号的零假设，我们使用组合估计。我们称这种新程序为 EFDR-CS，为了证明其有效性，我们展示了模拟研究的结果；我们在亚太地区的温度变化数据中引入聚合和不完整性的实验；以及对来自中东、阿富汗和巴基斯坦西部地区的卫星遥感数据的总二氧化碳柱的应用。本文的补充材料可在线获取。