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Improving Cramér-Rao Bound With Multivariate Parameters: An Extrinsic Geometry Perspective (2509.18978v1)
Published 23 Sep 2025 in math.ST, math.DG, math.PR, and stat.TH
Abstract: We derive a vector generalization of the square root embedding-based curvature-corrected Cram\'er--Rao bound (CRB) previously considered by the same author in \cite{srk} with scalar parameters. A \emph{directional} curvature correction is established first, and sufficient conditions for a conservative matrix-level CRB refinement are formulated using a simple semidefinite program. The directional correction theorem is rigorously illustrated with a Gaussian example.
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