### 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 language | English |
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Title of host publication | Geometric Science of Information - First International Conference, GSI 2013, Proceedings |

Pages | 721-728 |

Number of pages | 8 |

Volume | 8085 LNCS |

DOIs | |

Publication status | Published - 2013 |

Externally published | Yes |

Event | 1st International SEE Conference on Geometric Science of Information, GSI 2013 - Paris, France Duration: 2013 Aug 28 → 2013 Aug 30 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8085 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 1st International SEE Conference on Geometric Science of Information, GSI 2013 |
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Country | France |

City | Paris |

Period | 13/8/28 → 13/8/30 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Geometric Science of Information - First International Conference, GSI 2013, Proceedings*(Vol. 8085 LNCS, 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