Asymptotically efficient estimators for algebraic statistical manifolds

Kei Kobayashi, Henry P. Wynn

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it it shown how first and second order efficiency estimators can be constructed, such as bias corrected Maximum Likelihood Estimators and more general estimators, but for which the estimating equations are purely algebraic. In addition it is shown how Gröbner basis technology, which is at the heart of algebraic statistics, can be used to reduce the degrees of the terms in the estimating equations. This points the way to the feasible use, to find the estimators, of special methods for solving polynomial equations, such are homotopy methods.

Original languageEnglish
Title of host publicationGeometric Science of Information - First International Conference, GSI 2013, Proceedings
Pages721-728
Number of pages8
DOIs
Publication statusPublished - 2013 Oct 8
Externally publishedYes
Event1st International SEE Conference on Geometric Science of Information, GSI 2013 - Paris, France
Duration: 2013 Aug 282013 Aug 30

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8085 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other1st International SEE Conference on Geometric Science of Information, GSI 2013
CountryFrance
CityParis
Period13/8/2813/8/30

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Kobayashi, K., & Wynn, H. P. (2013). Asymptotically efficient estimators for algebraic statistical manifolds. In Geometric Science of Information - First International Conference, GSI 2013, Proceedings (pp. 721-728). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8085 LNCS). https://doi.org/10.1007/978-3-642-40020-9_80