Constrained Bayesian Method for Testing Equi-Correlation Coefficient
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’s approach, are examined. For the investigation of the obtained theoreti...
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MDPI AG
2024-10-01
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| author | Kartlos Kachiashvili Ashis SenGupta |
| author_facet | Kartlos Kachiashvili Ashis SenGupta |
| author_sort | Kartlos Kachiashvili |
| collection | DOAJ |
| description | 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’s 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’s 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. |
| format | Article |
| id | doaj-art-ed11ef8ad9684fb28cd1d244b8e47a81 |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-ed11ef8ad9684fb28cd1d244b8e47a812025-08-20T02:11:14ZengMDPI AGAxioms2075-16802024-10-01131072210.3390/axioms13100722Constrained Bayesian Method for Testing Equi-Correlation CoefficientKartlos Kachiashvili0Ashis SenGupta1Faculty of Informatics and Control Systems, Georgian Technical University, Tbilisi 0160, GeorgiaApplied Statistics Unit, Indian Statistical Institute, Kolkata 700108, IndiaThe 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’s 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’s 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.https://www.mdpi.com/2075-1680/13/10/722symmetric multivariate normal distributionhypothesisconstrained Bayesian methodBayes methodStein’s approach |
| spellingShingle | Kartlos Kachiashvili Ashis SenGupta Constrained Bayesian Method for Testing Equi-Correlation Coefficient Axioms symmetric multivariate normal distribution hypothesis constrained Bayesian method Bayes method Stein’s approach |
| title | Constrained Bayesian Method for Testing Equi-Correlation Coefficient |
| title_full | Constrained Bayesian Method for Testing Equi-Correlation Coefficient |
| title_fullStr | Constrained Bayesian Method for Testing Equi-Correlation Coefficient |
| title_full_unstemmed | Constrained Bayesian Method for Testing Equi-Correlation Coefficient |
| title_short | Constrained Bayesian Method for Testing Equi-Correlation Coefficient |
| title_sort | constrained bayesian method for testing equi correlation coefficient |
| topic | symmetric multivariate normal distribution hypothesis constrained Bayesian method Bayes method Stein’s approach |
| url | https://www.mdpi.com/2075-1680/13/10/722 |
| work_keys_str_mv | AT kartloskachiashvili constrainedbayesianmethodfortestingequicorrelationcoefficient AT ashissengupta constrainedbayesianmethodfortestingequicorrelationcoefficient |