论文标题
空间数据的渐近光谱理论
Asymptotic Spectral Theory for Spatial Data
论文作者
论文摘要
在本文中，我们研究了用于固定随机场的光谱分析（包括线性和非线性场）的渐近理论。傅立叶系数和周期图的渐近特性，包括傅立叶系数的限制分布，以及在各种温和条件下，在矩和依赖性结构的各种温和条件下获得了内核光谱估计量的均匀一致性。还建立了上述渐近渐近结果的有效性。
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.
