Abstract

Two primary concerns of inference for high-dimensional data are statistical accuracy and computational efficiency. Despite the appealing asymptotic properties of existing de-biasing methods, the de-biasing step is generally considered to be computationally intensive. In this article, we propose the constrained projection estimator (CPE) for deriving confidence intervals in a scalable and efficient way under high dimensions when the unknown parameters adopt an approximately sparse structure. The proposed method is implemented on the constrained projection spaces corresponding to the identifiable signals determined by a prescreening procedure, which significantly reduces the computational cost in comparison to the full de-biasing steps. Theoretically, we demonstrate that the proposed inference method enjoys equivalent asymptotic efficiency to the full de-biasing procedure in view of the lengths of confidence intervals. We demonstrate the scalability and effectiveness of the proposed method through simulation and real data studies.

摘要

高维数据推理的两个主要问题是统计准确性和计算效率。尽管现有去偏方法具有吸引人的渐近特性，但去偏步骤通常被认为是计算密集型的。在本文中，我们提出了约束投影估计器 (CPE)，用于在未知参数采用近似稀疏结构时以可扩展且高效的方式在高维度下推导置信区间。所提出的方法是在与预筛选程序确定的可识别信号相对应的受限投影空间上实施的，与完整的去偏置步骤相比，这显着降低了计算成本。理论上，我们证明，鉴于置信区间的长度，所提出的推理方法与完全去偏过程具有等效的渐近效率。我们通过模拟和真实数据研究证明了所提出方法的可扩展性和有效性。