空间数据的渐近Spectral Theory
Asymptotic Spectral Theory for Spatial Data
摘要：
本文研究平稳随机场（包括线性场和非线性场）谱分析的渐近理论。在各种关于矩和相依结构的温和条件下，得到了傅里叶系数和周期图的渐近性质，包括傅里叶系数的极限分布，以及核谱密度估计的一致相合性.上述渐近结果的有效性估计的空间领域也成立。
英文摘要：
In this paper we study the asymptotic theory for spectral analysis of stationary random fields, including linear and nonlinear fields. Asymptotic properties of Fourier coefficients and periodograms, including limiting distributions of Fourier coefficients, and the uniform consistency of kernel spectral density estimators are obtained under various mild conditions on moments and dependence structures. The validity of the aforementioned asymptotic results for estimated spatial fields is also established.
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