Spatially-referenced geostatistical responses that are collected in environmental sciences research are often subject to detection limits, where the measures are not fully quantifiable. This leads to censoring (left, right, interval, etc.), and various ad hoc statistical methods (such as choosing arbitrary detection limits, or data augmentation) are routinely employed during subsequent statistical analysis for inference and prediction. However, inference may be imprecise and sensitive to the assumptions and approximations involved in those arbitrary choices. To circumvent this, we propose an exact maximum likelihood estimation framework of the fixed effects and variance components and related prediction via a novel application of the Stochastic Approximation of the Expectation Maximization (SAEM) algorithm, allowing for easy and elegant estimation of model parameters under censoring. Both simulation studies and application to a real dataset on arsenic concentration collected by the Michigan Department of Environmental Quality demonstrate the advantages of our method over the available naïve techniques in terms of finite sample properties of the estimates, prediction, and robustness. The proposed methods can be implemented using the R package CensSpatial.

在环境科学研究中收集的以空间为参考的地统计响应通常受到检测极限的限制，在这些极限中，测量值无法完全量化。这导致检查（左，右，间隔等），并且在随后的统计分析过程中通常采用各种临时统计方法（例如选择任意检测极限或数据扩充）进行推断和预测。但是，推论可能是不精确的，并且对那些任意选择中涉及的假设和近似敏感。为了避免这种情况，我们提出了一个确切的建议固定效应和方差成分的最大似然估计框架，以及通过期望最大化的随机近似（SAEM）算法的新颖应用而进行的相关预测，可以在审查机制下轻松，优雅地估计模型参数。密歇根州环境质量部收集的模拟研究和对砷浓度的真实数据集的应用都证明了我们的方法在评估，预测和鲁棒性方面具有有限的样本性质，优于现有的纯朴技术。可以使用R包CensSpatial实现所提出的方法。