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題名 Compatibility of finite discrete conditional distributions 作者 Song, Chwan Chin
宋傳欽
Jiang, Tom J.
姜志銘
Li L.-A.
Chen C.-H.
Kuo K.-L.貢獻者 國立政治大學應用數學系 日期 2010 上傳時間 11-Jul-2010 15:58:41 (UTC+8) 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. 關聯 Statistica Sinica, 20, 423-440 資料類型 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
