The paper analyzes four classical signal-plus-noise models: the factor model, spiked sample covariance matrices, the sum of a Wigner matrix and a low-rank perturbation, and canonical correlation analysis with low-rank dependencies. The objective is to construct confidence intervals for the signal strength that are uniformly valid across all regimes - strong, weak, and critical signals. We demonstrate that traditional Gaussian approximations fail in the critical regime. Instead, we introduce a universal transitional distribution that enables valid inference across the entire spectrum of signal strengths. The approach is illustrated through applications in macroeconomics and finance.

翻译：本文分析了四种经典的信号加噪声模型：因子模型、尖峰样本协方差矩阵、Wigner矩阵与低秩扰动之和，以及具有低秩依赖关系的典型相关分析。研究目标在于构建对信号强度的置信区间，使其在强信号、弱信号和临界信号的所有区间内均保持统一有效性。我们证明传统的高斯近似方法在临界区间内失效。为此，我们引入了一种通用的过渡分布，能够在整个信号强度谱系中实现有效推断。该方法通过宏观经济和金融领域的应用案例进行说明。