A Unified Theory of Confidence Regions and Testing for High-Dimensional Estimating Equations
A Unified Theory of Confidence Regions and Testing for High-Dimensional Estimating Equations
复制标题
DOI：
10.1214/18-sts661
复制
发表时间：
2018-08-01
影响因子：
5.7
通讯作者：
Liu, Han
中科院分区：
文献类型：
--
作者：
Neykov, Matey;Ning, Yang;Liu, Han
我们提出了一个新的推论框架，用于在由高维估计方程式系统指定的统计模型中构建置信区和测试假设。我们通过将拟合估计方程投影到通过求解大规模线性程序获得的稀疏方向来构建影响函数。我们的主要理论贡献是为高维问题建立统一的Z估算理论。与现有方法不同的是，所有这些方法都需要规格的可能性或伪样的规格，我们的框架不含可能性。结果，我们的方法为一系列高维约束估计方程问题提供了有效的推断，而这些方程式问题不被现有方法涵盖。此类示例包括嘈杂的压缩传感，仪器变量回归，无方向的图形模型，判别分析和矢量自回旋模型。我们为所有这些示例提供了详细的理论结果。最后，我们进行了彻底的数值模拟和实际数据集分析，以支持开发的理论结果。
We propose a new inferential framework for constructing confidence regions and testing hypotheses in statistical models specified by a system of high-dimensional estimating equations. We construct an influence function by projecting the fitted estimating equations to a sparse direction obtained by solving a large-scale linear program. Our main theoretical contribution is to establish a unified Z-estimation theory of confidence regions for high-dimensional problems. Different from existing methods, all of which require the specification of the likelihood or pseudo-likelihood, our framework is likelihood-free. As a result, our approach provides valid inference for a broad class of high-dimensional constrained estimating equation problems, which are not covered by existing methods. Such examples include, noisy compressed sensing, instrumental variable regression, undirected graphical models, discriminant analysis and vector autoregressive models. We present detailed theoretical results for all these examples. Finally, we conduct thorough numerical simulations, and a real dataset analysis to back up the developed theoretical results.