This paper studies sparse covariance operator estimation for nonstationary Gaussian processes with sharply varying marginal variance and small correlation lengthscale. We introduce a covariance operator estimator that adaptively thresholds the sample covariance function using an estimate of the variance components. Building on recent results from empirical process theory, we derive an operator norm bound on the estimation error in terms of the sparsity level of the covariance and the expected supremum of the normalized process. Our theory and numerical simulations demonstrate the advantage of adaptive threshold estimators over universal threshold and sample covariance estimators in nonstationary settings.

翻译：本文研究了具有急剧变化的边缘方差和小相关长度尺度的非平稳高斯过程的稀疏协方差算子估计问题。我们提出了一种协方差算子估计器，该估计器利用方差分量的估计对样本协方差函数进行自适应阈值处理。基于经验过程理论的最新成果，我们推导了估计误差在算子范数意义下的界，该界由协方差的稀疏度水平与归一化过程的期望上确界所表征。我们的理论分析和数值模拟表明，在非平稳场景下，自适应阈值估计器相较于通用阈值估计器及样本协方差估计器具有显著优势。