Table of Contents
Scholarly Research Exchange
Volume 2009 (2009), Article ID 921574, 6 pages
http://dx.doi.org/10.3814/2009/921574
Research Article

Multiple Hypotheses LAO Testing for Many Independent Objects

Institute for Informatics and Automation Problems, Armenian National Academy of Sciences, 1 P. Sevak street, 0014 Yerevan, Armenia

Received 5 September 2008; Revised 27 May 2009; Accepted 15 July 2009

Copyright © 2009 Evgueni Haroutunian and Parandzem Hakobyan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The procedure of many hypotheses logarithmically asymptotically optimal (LAO) testing for a model consisting of three or more independent objects is analyzed. It is supposed that M probability distributions are known and each object follows one of them independently of others. The matrix of asymptotic interdependencies (reliability-reliability functions) of all possible pairs of the error probability exponents (reliabilities) in optimal testing for this model is studied. This problem was introduced (and solved for the case of two objects and two given probability distributions) by Ahlswede and Haroutunian; it is a generalization of two hypotheses LAO testing problem for one object investigated by Hoeffding, Csiszár and Longo, Tusnády, Longo and Sgarro, Birgé, and others.