We introduce methods for estimating the spectral density of a random field on a [Formula: see text]-dimensional lattice from incomplete gridded data. Data are iteratively imputed onto an expanded lattice according to a model with a periodic covariance function. The imputations are convenient computationally, in that circulant embedding and preconditioned conjugate gradient methods can produce imputations in [Formula: see text] time and [Formula: see text] memory. However, these so-called periodic imputations are motivated mainly by their ability to produce accurate spectral density estimates. In addition, we introduce a parametric filtering method that is designed to reduce periodogram smoothing bias. The paper contains theoretical results on properties of the imputed-data periodogram and numerical and simulation studies comparing the performance of the proposed methods to existing approaches in a number of scenarios. We present an application to a gridded satellite surface temperature dataset with missing values.

中文翻译：

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通过周期性嵌入对随机场进行谱密度估计

我们介绍了从不完整的网格数据估计[公式：见文本]维晶格上随机场的谱密度的方法。根据具有周期性协方差函数的模型，将数据迭代地输入到扩展的晶格上。插补在计算上很方便，因为循环嵌入和预处理共轭梯度方法可以在 [公式：参见文本] 时间和 [公式：参见文本] 内存中产生插补。然而，这些所谓的周期性插补主要是因为它们能够产生准确的谱密度估计。此外，我们介绍了一种旨在减少周期图平滑偏差的参数滤波方法。该论文包含有关估算数据周期图特性的理论结果，以及在多种情况下将所提出方法与现有方法的性能进行比较的数值和模拟研究。我们提出了一个应用于具有缺失值的网格化卫星表面温度数据集。