Nonparametric estimations and the diffeological Fisher metric

0544050 - MÚ 2022 RIV CH eng C - Conference Paper (international conference)
Le, Hong-Van - Tuzhilin, A. A.
Nonparametric estimations and the diffeological Fisher metric.
Geometric Structures of Statistical Physics, Information Geometry, and Learning. Cham: Springer, 2021 - (Barbaresco, F.; Nielsen, F.), s. 120-138. Springer Proceedings in Mathematics & Statistics, 361. ISBN 978-3-030-77956-6. ISSN 2194-1009.
[Statistical Physics, Information Geometry and Inference for Learning (SPIGL'20). Les Houches (FR), 27.07.2020-31.07.2020]
Institutional support: RVO:67985840
Keywords : Fisher metric * functorial language * probabilistic morphisms
OECD category: Pure mathematics
https://doi.org/10.1007/978-3-030-77957-3_7

In this paper, first, we survey the concept of diffeological Fisher metric and its naturality, using functorial language of probabilistic morphisms, and slightly extending Lê’s theory in [Le2020] to include weakly Ck-diffeological statistical models. Then we introduce the resulting notions of the diffeological Fisher distance, the diffeological Hausdorff–Jeffrey measure and explain their role in classical and Bayesian nonparametric estimation problems in statistics.
Permanent Link: http://hdl.handle.net/11104/0321109