In this paper, we investigate the adequacy testing problem of high-dimensional factor-augmented regression model. Existing test procedures perform not well under dense alternatives. To address this critical issue, we introduce a novel quadratic-type test statistic which can efficiently detect dense alternative hypotheses. We further propose an adaptive test procedure to remain powerful under both sparse and dense alternative hypotheses. Theoretically, under the null hypothesis, we establish the asymptotic normality of the proposed quadratic-type test statistic and asymptotic independence of the newly introduced quadratic-type test statistic and a maximum-type test statistic. We also prove that our adaptive test procedure is powerful to detect signals under either sparse or dense alternative hypotheses. Simulation studies and an application to an FRED-MD macroeconomics dataset are carried out to illustrate the merits of our introduced procedures.

翻译：本文研究了高维因子增强回归模型的充分性检验问题。现有检验方法在稠密备择假设下表现不佳。为解决这一关键问题，我们引入了一种新型二次型检验统计量，该统计量能有效检测稠密备择假设。我们进一步提出了一种自适应检验程序，使其在稀疏与稠密备择假设下均保持较高功效。在理论层面，我们证明了在原假设下所提二次型检验统计量的渐近正态性，以及新引入的二次型检验统计量与极大值型检验统计量间的渐近独立性。同时，我们证明了所提出的自适应检验程序在稀疏或稠密备择假设下均能有效检测信号。通过模拟研究及对FRED-MD宏观经济数据集的应用分析，验证了所提方法的优越性。