Top

Published in:

2024 | OriginalPaper | Chapter

An Ay-Lê-Jost-Schwachhöfer Type Characterization of Quantitatively Weakly Sufficient Statistics

Authors : Kaori Yamaguchi, Hiraku Nozawa

Published in: Differential Geometric Structures and Applications

Publisher: Springer Nature Switzerland

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

We explain the notion of a \(\delta \)-almost sufficient statistic, which is a quantitative weak version of sufficient statistics introduced in [11], based on the example of coin tosses. We review the basic notions in information geometry, e.g., parametrized measure models, statistics and Fisher quadratic forms. Then we state characterizations of sufficient statistics due to Ay-Jost-Lê-Schwachhöfer and an analogous characterizations of sufficient statistics due to [11].

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Smith-Gysin Sequence

next chapter Lower Bounds for High Derivatives of Smooth Functions With Given Zeros

Amari, S. and Nagaoka, H.: Methods of Information Geometry, Translated from the 1993 Japanese original by Daishi Harada. Transl. Math. Monogr. 191. American Mathematical Society, Providence, RI; Oxford University Press, Oxford, 2000

Ay, N., Jost, J., Lê, H.V. and Schwachhöfer, L.: Parametrized measure models, Bernoulli 24 (3) 1692–1725, (2015). https://doi.org/10.3150/16-BEJ910

Ay, N., Jost, J., Lê, H.V. and Schwachhöfer, L.: Information geometry and sufficient statistics, Probab. Theory Relat. Fields, 162 327–364, (2015). https://doi.org/10.1007/s00440-014-0574-8MathSciNetCrossRef

Ay, N., Jost, J., Lê, H.V. and Schwachhöfer, L.: Invariant Geometric Structures on Statistical Models. In: Nielsen, F., Barbaresco, F. (eds.) Geometric Science of Information. GSI 2015. LN in Computer Science, vol. 9389. Springer, Cham

Ay, N., Jost, J., Lê, H.V. and Schwachhöfer, L.: Information Geometry, Ergeb. Math. Grenzgeb. (3) Folge. A Series of Modern Surveys in Mathematics, 64. Springer, Cham, 2017

Ekeland, I.: The Hopf-Rinow theorem in infinite dimension, J. Diff. Geom. 13, no. 2, 287–301, (1978). https://doi.org/10.4310/jdg/1214434494MathSciNetCrossRef

Fisher, R. A.: On the mathematical foundations of theoretical statistics, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. containing Papers of a Mathematical or Physical Character, 222, 309–368. https://doi.org/10.1098/rsta.1922.0009

Hartmann, P. and Wintner, A.: On the Problems of Geodesics in the Small, Amer. J. Math. Vol. 73 132–148, (1951)MathSciNetCrossRef

Lê, H.V.: The uniqueness of the Fisher metric as information metric, Ann. Inst. Statist. Math. 69, no. 4, 879–896, (2017)MathSciNetCrossRef

10.

Neyman, J.: Sur un teorema concernente le considette statistiche sufficienti, Giorn. Istit. Ital. Att. 6, 320–334, (1935)

11.

Yamaguchi, K. and Nozawa, H.: On statistics which are almost sufficient from the viewpoint of the Fisher metrics, Preprint, arXiv:2305.04199 (2023)

Title: An Ay-Lê-Jost-Schwachhöfer Type Characterization of Quantitatively Weakly Sufficient Statistics
Authors: Kaori Yamaguchi
Hiraku Nozawa
Publisher: Springer Nature Switzerland
Book: Differential Geometric Structures and Applications
Print ISBN: 978-3-031-50585-0

Electronic ISBN: 978-3-031-50586-7

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-50586-7_13

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"