Vol. 11, No. 2, 2020
Download this article
Download this article For screen
For printing
Recent Issues
Volume 15, Issue 2
Volume 15, Issue 1
Volume 14, Issue 2
Volume 14, Issue 1
Volume 13, Issue 1
Volume 12, Issue 2
Volume 12, Issue 1
Volume 11, Issue 2
Volume 11, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN 2693-3004 (online)
ISSN 2693-2997 (print)
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Holonomic gradient method for two-way contingency tables

Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama and Nobuki Takayama
Vol. 11 (2020), No. 2, 125–153
DOI: 10.2140/astat.2020.11.125
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.

PDF Access Denied

We have not been able to recognize your IP address 18.97.9.175 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

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