Spatially misaligned data, where the response and covariates are observed at different spatial locations, commonly arise in many environmental studies. Much of the statistical literature on handling spatially misaligned data has been devoted to the case of a single covariate and a linear relationship between the response and this covariate. Motivated by spatially misaligned data collected on air pollution and weather in China, we propose a cokrig-and-regress (CNR) method to estimate spatial regression models involving multiple covariates and potentially non-linear associations. The CNR estimator is constructed by replacing the unobserved covariates (at the response locations) by their cokriging predictor derived from the observed but misaligned covariates under a multivariate Gaussian assumption, where a generalized Kronecker product covariance is used to account for spatial correlations within and between covariates. A parametric bootstrap approach is employed to bias-correct the CNR estimates of the spatial covariance parameters and for uncertainty quantification. Simulation studies demonstrate that CNR outperforms several existing methods for handling spatially misaligned data, such as nearest-neighbor interpolation. Applying CNR to the spatially misaligned air pollution and weather data in China reveals a number of non-linear relationships between PM$_{2.5}$ concentration and several meteorological covariates.

翻译：空间错位数据（即响应变量与协变量在不同空间位置观测到的数据）在环境研究中普遍存在。现有处理空间错位数据的统计学文献大多聚焦于单一协变量及响应变量与协变量间的线性关系。受中国空气污染与气象空间错位数据的启发，我们提出一种协克里金-回归（CNR）方法，用于估计包含多个协变量及潜在非线性关联的空间回归模型。CNR估计量通过将观测但错位的协变量在多元高斯假设下推导的协克里金预测值（采用广义Kronecker积协方差结构表征协变量内部及之间的空间相关性）替换响应位置处未观测的协变量来构建。采用参数自助法对空间协方差参数的CNR估计进行偏差校正与不确定性量化。仿真研究表明，CNR在空间错位数据处理方面优于最近邻插值等现有方法。将CNR应用于中国空间错位的空气污染与气象数据，揭示了PM$_{2.5}$浓度与多个气象协变量之间的非线性关系。