{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:30:53Z","timestamp":1760146253198,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T00:00:00Z","timestamp":1729123200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The problem of testing the equi-correlation coefficient of a standard symmetric multivariate normal distribution is considered. Constrained Bayesian and classical Bayes methods, using the maximum likelihood estimation and Stein\u2019s approach, are examined. For the investigation of the obtained theoretical results and choosing the best among them, different practical examples are analyzed. The simulation results showed that the constrained Bayesian method (CBM) using Stein\u2019s approach has the advantage of making decisions with higher reliability for testing hypotheses concerning the equi-correlation coefficient than the Bayes method. Also, the use of this approach with the probability distribution of linear combinations of chi-square random variables gives better results compared to that of using the integrated probability distributions in terms of providing both the necessary precisions as well as convenience of implementation in practice. Recommendations towards the use of the proposed methods for solving practical problems are given.<\/jats:p>","DOI":"10.3390\/axioms13100722","type":"journal-article","created":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T11:19:18Z","timestamp":1729163958000},"page":"722","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Constrained Bayesian Method for Testing Equi-Correlation Coefficient"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5313-5991","authenticated-orcid":false,"given":"Kartlos","family":"Kachiashvili","sequence":"first","affiliation":[{"name":"Faculty of Informatics and Control Systems, Georgian Technical University, Tbilisi 0160, Georgia"},{"name":"Ilia Vekua Institute of Applied Mathematics, Ivane Javakhishvili Tbilisi State University, Tbilisi 0186, Georgia"},{"name":"Muskhelishvili Institute of Computational Mathematics, Georgian Technical University, Tbilisi 0159, Georgia"}]},{"given":"Ashis","family":"SenGupta","sequence":"additional","affiliation":[{"name":"Applied Statistics Unit, Indian Statistical Institute, Kolkata 700108, India"},{"name":"Medical College of Georgia, Augusta University, Augusta, GA 30912, USA"},{"name":"Department of Statistics, Middle East Technical University, 06800 Ankara, Turkey"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1111\/j.1467-842X.1987.tb00720.x","article-title":"On Tests for Equi-correlation Coefficient of a Standard Symmetric Multivariate Normal Distribution","volume":"29","author":"SenGupta","year":"1987","journal-title":"Aust. 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