An Asymptotic Two-Sided Test in a Family of Multivariate Distribution
In the present paper, a two-sided test in a family of multivariate distribution according to the Mahalanobis distance with mean vector and positive definite matrix is considered. First, a family of multivariate distribution is introduced, then using the likelihood ratio method a test statistic is co...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Springer
2020-05-01
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| Series: | Journal of Statistical Theory and Applications (JSTA) |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/125940938/view |
| _version_ | 1818160902467223552 |
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| author | Abouzar Bazyari Mahmoud Afshari Monjed H. Samuh |
| author_facet | Abouzar Bazyari Mahmoud Afshari Monjed H. Samuh |
| author_sort | Abouzar Bazyari |
| collection | DOAJ |
| description | In the present paper, a two-sided test in a family of multivariate distribution according to the Mahalanobis distance with mean vector and positive definite matrix is considered. First, a family of multivariate distribution is introduced, then using the likelihood ratio method a test statistic is computed. The distribution of the test statistic is proposed for different sample sizes and fixed dimension. We study the distribution approximation computed using the likelihood ratio test and an efficient algorithm to compute the density functions can be derived according to Witkovsk´y, J. Stat. Plan. Inference. 94 (2001), 1–13. Also, a simulation study is presented on the sample sizes and powers to compare the performance of tests and show that the proposed distribution approximation is better than the classical distribution approximation. |
| first_indexed | 2024-12-11T16:09:15Z |
| format | Article |
| id | doaj.art-c0c38eecb8ca49f5973954933117ed3d |
| institution | Directory Open Access Journal |
| issn | 2214-1766 |
| language | English |
| last_indexed | 2024-12-11T16:09:15Z |
| publishDate | 2020-05-01 |
| publisher | Springer |
| record_format | Article |
| series | Journal of Statistical Theory and Applications (JSTA) |
| spelling | doaj.art-c0c38eecb8ca49f5973954933117ed3d2022-12-22T00:59:07ZengSpringerJournal of Statistical Theory and Applications (JSTA)2214-17662020-05-0119210.2991/jsta.d.200511.001An Asymptotic Two-Sided Test in a Family of Multivariate DistributionAbouzar BazyariMahmoud AfshariMonjed H. SamuhIn the present paper, a two-sided test in a family of multivariate distribution according to the Mahalanobis distance with mean vector and positive definite matrix is considered. First, a family of multivariate distribution is introduced, then using the likelihood ratio method a test statistic is computed. The distribution of the test statistic is proposed for different sample sizes and fixed dimension. We study the distribution approximation computed using the likelihood ratio test and an efficient algorithm to compute the density functions can be derived according to Witkovsk´y, J. Stat. Plan. Inference. 94 (2001), 1–13. Also, a simulation study is presented on the sample sizes and powers to compare the performance of tests and show that the proposed distribution approximation is better than the classical distribution approximation.https://www.atlantis-press.com/article/125940938/viewAsymptotic two-sided testChi-squared distributionEfficient algorithmMultivariate distribution elements |
| spellingShingle | Abouzar Bazyari Mahmoud Afshari Monjed H. Samuh An Asymptotic Two-Sided Test in a Family of Multivariate Distribution Journal of Statistical Theory and Applications (JSTA) Asymptotic two-sided test Chi-squared distribution Efficient algorithm Multivariate distribution elements |
| title | An Asymptotic Two-Sided Test in a Family of Multivariate Distribution |
| title_full | An Asymptotic Two-Sided Test in a Family of Multivariate Distribution |
| title_fullStr | An Asymptotic Two-Sided Test in a Family of Multivariate Distribution |
| title_full_unstemmed | An Asymptotic Two-Sided Test in a Family of Multivariate Distribution |
| title_short | An Asymptotic Two-Sided Test in a Family of Multivariate Distribution |
| title_sort | asymptotic two sided test in a family of multivariate distribution |
| topic | Asymptotic two-sided test Chi-squared distribution Efficient algorithm Multivariate distribution elements |
| url | https://www.atlantis-press.com/article/125940938/view |
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