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| Title | Compatibility of finite discrete conditional distributions |
| Creator | Song, Chwan Chin 宋傳欽 Jiang, Tom J. 姜志銘 Li L.-A. Chen C.-H. Kuo K.-L. |
| Contributor | 國立政治大學應用數學系 |
| Date | 2010 |
| Date Issued | 11-Jul-2010 15:58:41 (UTC+8) |
| Summary | This paper provides new versions of necessary and sufficient conditions for compatibility of finite discrete conditional distributions, and of the uniqueness for those compatible conditional distributions. We note that the ratio matrix (the matrix C in Arnold and Press (1989)), after interchanging its rows and/or columns, can be rearranged to be an irreducible block diagonal matrix. We find that checking compatibility is equivalent to inspecting whether every block on the diagonal has a rank one positive extension, and that the necessary and sufficient conditions of the uniqueness, if the given conditional densities are compatible, is that the ratio matrix itself is irreducible. We show that each joint density, if it exists, corresponds to a rank one positive extension of the ratio matrix, and we characterize the set of all possible joint densities. Finally, we provide algorithms for checking compatibility, for checking uniqueness, and for constructing densities. |
| Relation | Statistica Sinica, 20, 423-440 |
| Type | article |
| dc.contributor | 國立政治大學應用數學系 | en_US |
| dc.creator (作者) | Song, Chwan Chin | en_US |
| dc.creator (作者) | 宋傳欽 | - |
| dc.creator (作者) | Jiang, Tom J. | en_US |
| dc.creator (作者) | 姜志銘 | zh_TW |
| dc.creator (作者) | Li L.-A. | en_US |
| dc.creator (作者) | Chen C.-H. | en_US |
| dc.creator (作者) | Kuo K.-L. | en_US |
| dc.date (日期) | 2010 | en_US |
| dc.date.accessioned | 11-Jul-2010 15:58:41 (UTC+8) | - |
| dc.date.available | 11-Jul-2010 15:58:41 (UTC+8) | - |
| dc.date.issued (上傳時間) | 11-Jul-2010 15:58:41 (UTC+8) | - |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/42371 | - |
| dc.description.abstract (摘要) | This paper provides new versions of necessary and sufficient conditions for compatibility of finite discrete conditional distributions, and of the uniqueness for those compatible conditional distributions. We note that the ratio matrix (the matrix C in Arnold and Press (1989)), after interchanging its rows and/or columns, can be rearranged to be an irreducible block diagonal matrix. We find that checking compatibility is equivalent to inspecting whether every block on the diagonal has a rank one positive extension, and that the necessary and sufficient conditions of the uniqueness, if the given conditional densities are compatible, is that the ratio matrix itself is irreducible. We show that each joint density, if it exists, corresponds to a rank one positive extension of the ratio matrix, and we characterize the set of all possible joint densities. Finally, we provide algorithms for checking compatibility, for checking uniqueness, and for constructing densities. | - |
| dc.language | en | en_US |
| dc.language.iso | en_US | - |
| dc.relation (關聯) | Statistica Sinica, 20, 423-440 | - |
| dc.title (題名) | Compatibility of finite discrete conditional distributions | en_US |
| dc.type (資料類型) | article | en |