2017/03/28 by Jürgen Jost, Jost, Jürgen, Hông Vân Lê +3
Engineering · Mathematics · Physics and Astronomy · #62G07 #62H12 #FOS: Mathematics #Probability (math.PR) #Sparse and Compressive Sensing Techniques #Statistical Mechanics and Entropy #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1703.09403
openalex publication_date 2017/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notion of the essential tangent bundle of a parametrized measure model and the notion of reduced Fisher metric on a (possibly singular) 2-integrable measure model. Using these notions and a new characterization of k-integrable parametrized measure models, we extend the Cramér-Rao inequality to 2-integrable (possibly singular) statistical models for general φ-estimations, where φ is a V-valued feature function and V is a topological vector space. Thus we derive an intrinsic Cramér-Rao inequality in the most general terms of parametric statistics.