On Higher-Order Geometric Refinements of Classical Covariance Asymptotics: An Approach via Intrinsic and Extrinsic Information Geometry
经典协方差渐近的高阶几何精化：内在与外在信息几何方法
Classical Fisher-information asymptotics describe the covariance of regular efficient estimators through the local quadratic approximation of the log-likelihood, and thus capture first-order geometry only. In curved models, including mixtures, curved exponential families, latent-variable models, and manifold-constrained parameter spaces, finite-sample behavior can deviate systematically from these predictions. We develop a coordinate-invariant, curvature-aware refinement by…