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.
翻译:减少尺寸是分析高维数据的一个重要工具。预测信封是回归的维度减少方法,它假定预测器的某些线性组合与回归无关。该方法可大大提高对传统最大可能性和最小方形估计数的估算效率和预测准确性。虽然为独立数据开发了预测信封并进行了研究,但没有进行使预测信封与空间数据相适应的工作。在这项工作中,预测信封适应流行的空间空间模型以形成空间预测信封(SPE) 。 SPE的最大可能性估计数是连同某些假设的估计数的无症状分布一起得出的,表明SPE估计数比原始空间模型的估计数要简单有效。通过模拟研究和对地球化学数据集的分析来说明拟议模型的有效性。