Reliable reconstruction of missing observations in environmental panel datasets is essential for accurate exposure assessment and policy analysis. Traditional nuclear norm matrix completion methods effectively impute missing entries in low-rank matrices, yet often overlook the spatial dependence inherent to air quality processes. This paper introduces the Eigenvector Spatial Filters Nuclear Norm Matrix Completion (ESFNNMC) method, an extension of nuclear norm fixed-effects matrix completion that replaces unit-specific intercepts with a set of Moran-type eigenvectors capturing spatial autocorrelation in the data. To estimate the model, we propose a Block-Coordinate Descent (BCD) approach for multiconvex optimization problems, with soft-thresholded singular value decomposition and cross-validated regularization. Through comprehensive simulations varying missingness patterns, the level of spatial and temporal autocorrelation, and dimension, shape, and rank structure of the matrices, ESFNNMC demonstrates substantial improvements in imputation accuracy over the standard fixed-effects approach, while keeping the computational cost approximately unchanged. The method is applied to impute missing entries in daily PM10 measurements in 64 monitoring stations in Lombardy, Italy, during the year 2021.

翻译：环境面板数据中缺失观测的可靠重建对于精确暴露评估和政策分析至关重要。传统的核范数矩阵补全方法能有效填补低秩矩阵中的缺失条目，但往往忽视了空气质量过程中固有的空间依赖性。本文提出特征向量空间滤波核范数矩阵补全（ESFNNMC）方法，该方法是对核范数固定效应矩阵补全的扩展，用一组捕捉数据空间自相关性的Moran型特征向量替代单位特定截距项。为估计模型，我们提出了一种针对多凸优化问题的分块坐标下降（BCD）方法，结合软阈值奇异值分解和交叉验证正则化。通过综合模拟不同缺失模式、空间与时间自相关性水平以及矩阵的维度、形状和秩结构，ESFNNMC在保持计算成本大致不变的同时，相比标准固定效应方法展现出显著的插补精度提升。该方法被应用于填补2021年意大利伦巴第大区64个监测站每日PM10测量值中的缺失条目。