This paper proposes a general two directional simultaneous inference (TOSI) framework for high-dimensional models with a manifest variable or latent variable structure, for example, high-dimensional mean models, high-dimensional sparse regression models, and high-dimensional latent factors models. TOSI performs simultaneous inference on a set of parameters from two directions, one to test whether the assumed zero parameters indeed are zeros and one to test whether exist zeros in the parameter set of nonzeros. As a result, we can exactly identify whether the parameters are zeros, thereby keeping the data structure fully and parsimoniously expressed. We theoretically prove that the proposed TOSI method asymptotically controls the Type I error at the prespecified significance level and that the testing power converges to one. Simulations are conducted to examine the performance of the proposed method in finite sample situations and two real datasets are analyzed. The results show that the TOSI method is more predictive and has more interpretable estimators than existing methods.

翻译：本文针对具有显变量或潜变量结构的高维模型（例如高维均值模型、高维稀疏回归模型和高维潜在因子模型），提出了一种通用的双向同时推断（TOSI）框架。TOSI从两个方向对参数集进行同时推断：一方面检验假定为零的参数是否确实为零，另一方面检验非零参数集中是否存在零值。通过这种方式，我们能够精确识别参数是否为零，从而在充分表达数据结构的同时保持模型简洁性。理论上，我们证明了所提出的TOSI方法能够渐进地将第一类错误控制在预设显著性水平内，且检验功效趋近于1。通过仿真实验评估了该方法在有限样本下的表现，并分析了两个真实数据集。结果表明，相较于现有方法，TOSI方法具有更强的预测能力和更易解释的估计量。