Local Optimality and Rigidity of Frobenius Tests for Dense High-Dimensional Covariance Alternatives
稠密高维协方差备择下 Frobenius 检验的局部最优性与刚性
We study identity testing for high-dimensional covariance matrices against dense alternatives of unknown direction, with $p/n \to γ$. Along a globally positive quadratic precision path, mixing Gaussian alternatives over a Gaussian Orthogonal Ensemble direction yields a contiguous experiment whose log likelihood reduces to the corrected Frobenius statistic; its upper-tail test attains the limiting weighted-power envelope at every fixed strength. Fixing the prior's Frobenius…