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math.ST2026
Refining Cramér-Rao Bound With Multivariate Parameters: An Extrinsic Geometry Perspective
Sunder Ram Krishnan
We derive a vector generalization of the curvature-corrected Cramér--Rao bound (CRB) in the nonasymptotic regime using a Hilbert space square-root embedding. Building on previous…
math.ST2026
Improving Cramér-Rao Bound And Its Variants: An Extrinsic Geometry Perspective
Sunder Ram Krishnan
This work presents a geometric refinement of the classical Cramér--Rao bound (CRB) in the non-asymptotic regime by incorporating curvature-aware corrections based on the second fu…
math.ST2025
Cartan meets Cramér-Rao
Sunder Ram Krishnan
A Cartan-geometric, jet bundle formulation of curvature-aware variance bounds in parametric statistical estimation is developed. Building on our earlier extrinsic Hilbert space app…