Spectral methods for nonstationary spatial processes
Spectral methods for nonstationary spatial processes
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DOI：
10.1093/biomet/89.1.197
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发表时间：
2002-03-01
期刊：
影响因子：
2.7
通讯作者：
Fuentes, M
中科院分区：
文献类型：
--
作者：
Fuentes, M
我们提出了一个非平稳周期图和各种参数的方法来估计一个非平稳空间过程的谱密度。我们还研究了通过收缩渐近估计的渐近性质，假设相邻观测之间的距离趋于零的大小的观测区域的增长没有约束。使用这种类型的渐近模型，我们可以唯一地确定谱密度，避免混淆问题。我们还提出了一类新的非平稳过程，基于卷积的本地平稳过程。该模型的优点是，该模型是同时定义无处不在，不像“移动窗口”的方法，但它保留了有吸引力的属性，局部在小区域，它的行为像一个固定的空间过程。应用包括美国环境保护局提供的空气污染数据的空间分析和建模。
We propose a nonstationary periodogram and various parametric approaches for estimating the spectral density of a nonstationary spatial process. We also study the asymptotic properties of the proposed estimators via shrinking asymptotics, assuming the distance between neighbouring observations tends to zero as the size of the observation region grows without bound. With this type of asymptotic model we can uniquely determine the spectral density, avoiding the aliasing problem. We also present a new class of nonstationary processes, based on a convolution of local stationary processes. This model has the advantage that the model is simultaneously defined everywhere, unlike 'moving window' approaches, but it retains the attractive property that, locally in small regions, it behaves like a stationary spatial process. Applications include the spatial analysis and modelling of air pollution data provided by the US Environmental Protection Agency.