Vol. 11, No. 2, 2020

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Holonomic gradient method for two-way contingency tables

Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama and Nobuki Takayama

Vol. 11 (2020), No. 2, 125–153
Abstract

The holonomic gradient method gives an algorithm to efficiently and accurately evaluate normalizing constants and their derivatives. We apply the holonomic gradient method in the case of the conditional Poisson or multinomial distribution on two-way contingency tables. We utilize the modular method in computer algebra or some other tricks for an efficient and exact evaluation, and we compare them and discuss on their implementation. We also discuss on a theoretical aspect of the distribution from the viewpoint of the conditional maximum likelihood estimation. We decompose parameters of interest and nuisance parameters in terms of sigma algebras for general two-way contingency tables with arbitrary zero cell patterns.

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Keywords
holonomic gradient method, two-way contingency tables, modular method, conditional maximum likelihood estimation
Mathematical Subject Classification 2010
Primary: 33C90, 65Q10, 62B05, 62H17
Milestones
Received: 14 June 2018
Revised: 5 January 2020
Accepted: 24 March 2020
Published: 28 December 2020
Authors
Yoshihito Tachibana
Kobe University
Kobe 657-8501
Japan
Yoshiaki Goto
Otaru University of Commerce
Otaru 047-8501
Japan
Tamio Koyama
Wakkanai Hokusei Gakuen University
Wakkanai 097-0013
Japan
Nobuki Takayama
Kobe University
Kobe 657-8501
Japan