高维稠密效应线性模型中可解释变异的统计推断
Statistical Inference on Explained Variation in High-dimensional Linear Model with Dense Effects
摘要：
通过一组协变量对结果的解释变异进行统计推断在实践中特别有意义。当协变量为中高维且效应不稀疏时，已经提出了几种估计和推断方法。现有的方法的一个主要问题是，推理过程是不稳健的正态假设的协变量和残差。本文提出了一种估计方程方法来估计和推断高维线性模型中被解释的变异。与现有的方法不同，所提出的方法不依赖于限制性的正态性假设的推断。在合理的条件下，证明了所提出的估计量是相合的且渐近正态分布的。仿真研究表明，与现有的方法相比，所提出的推理过程具有更好的性能。所提出的方法被应用到研究的变化，由环境污染物解释的糖化血红蛋白在全国健康和营养检查调查数据集。
英文摘要：
Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been proposed for estimation and inference. One major problem with the existing approaches is that the inference procedures are not robust to the normality assumption on the covariates and the residual errors. In this paper, we propose an estimating equation approach to the estimation and inference on the explained variation in the high-dimensional linear model. Unlike the existing approaches, the proposed approach does not rely on the restrictive normality assumptions for inference. It is shown that the proposed estimator is consistent and asymptotically normally distributed under reasonable conditions. Simulation studies demonstrate better performance of the proposed inference procedure in comparison with the existing approaches. The proposed approach is applied to studying the variation of glycohemoglobin explained by environmental pollutants in a National Health and Nutrition Examination Survey data set.
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