Spatial Linear Regression with Covariate Measurement Errors: Inference and Scalable Computation in a Functional Modeling Approach
针对空间线性模型中协变量存在测量误差导致估计偏倚的问题，提出基于无偏估计方程的函数建模方法，证明估计量一致性并给出可扩展计算算法，适用于北极海冰等空间数据分析。
For spatial linear models, the classical maximum-likelihood estimators of both regression coefficients and variance components can be biased when the covariates are measured with errors. This work introduces a theoretically backed-up estimation framework for the spatial linear errors-in-variables model in a functional approach. Compared with the structural models, the functional approach treats the unobserved true covariates as fixed unknown parameters without imposing additional structures, thus leading to more robust parameter inference. Our model parameters are estimated simultaneously based on a set of unbiased estimating equations. Under some regularity conditions, we prove the consistency of the proposed estimating-equation estimators and derive their asymptotic distribution. In addition, a consistent variance estimator is developed for the estimating-equation estimators. To handle large spatial datasets, we provide two approaches to obtain scalable estimations based on our proposed estimating equations, where the required computational time and storage are reduced to be linear with sample size for each estimating-function evaluation. Simulation studies under different settings show that our estimators are consistent and the scalable algorithms work well. Finally, the proposed method is applied to studying the relationship between Arctic sea ice and related geophysical variables. Supplementary materials for this article are available online.