In this paper, we present a new and effective simulation-based approach to conduct both finite- and large-sample inference for high-dimensional linear regression models. This approach is developed under the so-called repro samples framework, in which we conduct statistical inference by creating and studying the behavior of artificial samples that are obtained by mimicking the sampling mechanism of the data. We obtain confidence sets for (a) the true model corresponding to the nonzero coefficients, (b) a single or any collection of regression coefficients, and (c) both the model and regression coefficients jointly. We also extend our approaches to drawing inferences on functions of the regression coefficients. The proposed approach fills in two major gaps in the high-dimensional regression literature: (1) lack of effective approaches to address model selection uncertainty and provide valid inference for the underlying true model; (2) lack of effective inference approaches that guarantee finite-sample performances. We provide both finite-sample and asymptotic results to theoretically guarantee the performances of the proposed methods. In addition, our numerical results demonstrate that the proposed methods are valid and achieve better coverage with smaller confidence sets than the existing state-of-art approaches, such as debiasing and bootstrap approaches.
翻译:在本文中,我们提出了一个新的、有效的模拟模拟法方法,用于对高维线性回归模型进行有限和大成成像的测算,这是对高维线性回归模型进行定量和大成成模的假设的新的、有效的模拟法,这是在所谓的再处理抽样样本框架内开发的,我们通过模拟数据取样机制的模拟获得的人工样品的行为进行统计推断,在这种框架内,我们通过建立和研究通过模拟数据抽样机制获得的人工样品的行为来进行统计推断;我们为以下(a) 与非零系数相对的真实模型,(b) 单一或任何回归系数的单一或任何集合,以及(c) 模型和回归系数共同进行。我们还将我们的方法扩大到对回归系数的功能进行推断,我们还在所谓的再扩展了我们的方法,对模型和回归系数和回归系数共同进行扩展了我们的方法,对回归系数系数系数系数作了推推推推,在高位回归率回归率文献文献文献中,拟议的方法填补了两个主要的两大缺陷:(1) 缺乏解决模型选择的不确定性的有效方法,并为基本真实模型模型提供有效的推断模型;(2) 缺乏保证有限性性性性性性性性工作的有效推断方法,我们提供有限的微结果,从理论上保证拟议方法,比小的测船床床底方法,实现更好的方法,比小的测方法。