Affine Gateaux Differentials and the von Mises Statistical Calculus

2024/03/12 by Simone Cerreia‐Vioglio, Fabio Maccheroni, Cerreia-Vioglio, Simone +7
Physics and Astronomy · #26B25 #26E15 #49J50 #49J52 #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2403.07827

openalex publication_date 2024/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents a general study of one-dimensional differentiability for functionals defined on convex domains that are not necessarily open. The local approximation is carried out using affine functionals, as opposed to linear functionals typically employed in standard Gateaux differentiability. This affine notion of differentiability naturally arises in certain applications and has been utilized by some authors in the statistics literature. We aim to offer a unified and comprehensive perspective on this concept.

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