论文标题
空间相关数据的尺寸降低：空间预测器包膜
Dimension Reduction for Spatially Correlated Data: Spatial Predictor Envelope
论文作者
论文摘要
降低是分析高维数据的重要工具。预测变量包络是一种减小回归尺寸的方法，该方法假设预测因子的某些线性组合与回归无关。该方法可能会导致估计效率和预测准确性比传统的最大可能性和最小二乘估计值获得可观的提高。尽管已经开发并研究了用于独立数据的预测函数信封，但尚未完成调整预测器信封对空间数据的工作。在这项工作中，预测变量包络适应了流行的空间模型，以形成空间预测器包膜（SPE）。得出了SPE的最大似然估计，以及给定某些假设的估计值的渐近分布，表明SPE估计值比原始空间模型的估计值更有效。通过模拟研究和地理化学数据集的分析来说明所提出模型的有效性。
Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the regression. The method can result in substantial gains in estimation efficiency and prediction accuracy over traditional maximum likelihood and least squares estimates. While predictor envelopes have been developed and studied for independent data, no work has been done adapting predictor envelopes to spatial data. In this work, the predictor envelope is adapted to a popular spatial model to form the spatial predictor envelope (SPE). Maximum likelihood estimates for the SPE are derived, along with asymptotic distributions for the estimates given certain assumptions, showing the SPE estimates to be asymptotically more efficient than estimates of the original spatial model. The effectiveness of the proposed model is illustrated through simulation studies and the analysis of a geo-chemical data set.
