In this paper, we address the problem of predicting a response variable in the context of both, spatially correlated and high-dimensional data. To reduce the dimensionality of the predictor variables, we apply the sufficient dimension reduction (SDR) paradigm, which reduces the predictor space while retaining relevant information about the response. To achieve this, we impose two different spatial models on the inverse regression: the separable spatial covariance model (SSCM) and the spatial autoregressive error model (SEM). For these models, we derive maximum likelihood estimators for the reduction and use them to predict the response via nonparametric rules for forward regression. Through simulations and real data applications, we demonstrate the effectiveness of our approach for spatial data prediction.

翻译：本文研究了在空间相关和高维数据背景下预测响应变量的问题。为降低预测变量的维度，我们采用充分降维范式，在保留响应变量相关信息的同时缩减预测空间。为实现这一目标，我们在逆回归中施加了两种不同的空间模型：可分离空间协方差模型与空间自回归误差模型。针对这些模型，我们推导了降维的最大似然估计量，并利用前向回归的非参数规则进行响应预测。通过仿真实验与真实数据应用，我们验证了所提方法在空间数据预测中的有效性。