Fixed-Domain Asymptotics for Spatial Periodograms
Fixed-Domain Asymptotics for Spatial Periodograms
复制标题
空间周期图的固定域渐近
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
M. Stein
中科院分区：
文献类型：
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作者：
M. Stein
摘要周期图常被用来估计空间过程的谱密度。这种估计的基础是周期图通常具有的两个渐近性质：（1）特定频率处的周期图对于谱密度近似无偏，以及（2）不同频率处的周期图的相关性近似为零。对于空间数据，通常使用固定域渐近性是合适的，其中观测值在某些固定区域中随着其数量的增加而变得越来越密集。使用固定域渐近，这篇文章表明，标准的渐近结果周期图不适用，使用原始数据的周期图可以产生高度误导的结果。但是，通过在计算周期图之前适当地过滤数据，可以获得与空间周期图的标准渐近结果类似的结果。
Abstract The periodogram for a spatial process observed on a lattice is often used to estimate the spectral density. The bases for such estimators are two asymptotic properties that periodograms commonly possess: (1) the periodogram at a particular frequency is approximately unbiased for the spectral density, and (2) the correlation of the periodogram at distinct frequencies is approximately zero. For spatial data, it is often appropriate to use fixed-domain asymptotics in which the observations get increasingly dense in some fixed region as their number increases. Using fixed-domain asymptotics, this article shows that standard asymptotic results for periodograms do not apply and that using the periodogram of the raw data can yield highly misleading results. But by appropriately filtering the data before computing the periodogram, it is possible to obtain results similar to the standard asymptotic results for spatial periodograms.