LEADER 03197nam 22005895 450 001 9910483158003321 005 20250609110604.0 010 $a981-15-6975-4 024 7 $a10.1007/978-981-15-6975-3 035 $a(CKB)4100000011354894 035 $a(DE-He213)978-981-15-6975-3 035 $a(MiAaPQ)EBC6272274 035 $a(PPN)258305088 035 $a(MiAaPQ)EBC6270899 035 $a(EXLCZ)994100000011354894 100 $a20200717d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStatistics Based on Dirichlet Processes and Related Topics /$fby Hajime Yamato 205 $a1st ed. 2020. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2020. 215 $a1 online resource (VIII, 74 p. 7 illus.) 225 1 $aJSS Research Series in Statistics,$x2364-0065 300 $aIncludes index. 311 08$a981-15-6974-6 327 $aIntroduction -- Dirichlet process and Chinese restaurant process -- Nonparametric estimation of estimable parameter -- Random partition of positive integer. 330 $aThis book focuses on the properties associated with the Dirichlet process, describing its use a priori for nonparametric inference and the Bayes estimate to obtain limits for the estimable parameter. It presents the limits and the well-known U- and V-statistics as a convex combination of U-statistics, and by investigating this convex combination, it demonstrates these three statistics. Next, the book notes that the Dirichlet process gives the discrete distribution with probability one, even if the parameter of the process is continuous. Therefore, there are duplications among the sample from the distribution, which are discussed. Because sampling from the Dirichlet process is described sequentially, it can be described equivalently by the Chinese restaurant process. Using this process, the Donnelly?Tavaré?Griffiths formulas I and II are obtained, both of which give the Ewens? samplingformula. The book then shows the convergence and approximation of the distribution for its number of distinct components. Lastly, it explains the interesting properties of the Griffiths?Engen?McCloskey distribution, which is related to the Dirichlet process and the Ewens? sampling formula. 410 0$aJSS Research Series in Statistics,$x2364-0065 606 $aStatistics 606 $aStatistics 606 $aMathematical statistics 606 $aApplied Statistics 606 $aStatistical Theory and Methods 606 $aMathematical Statistics 615 0$aStatistics. 615 0$aStatistics. 615 0$aMathematical statistics. 615 14$aApplied Statistics. 615 24$aStatistical Theory and Methods. 615 24$aMathematical Statistics. 676 $a331.257094 700 $aYamato$b Hajime$4aut$4http://id.loc.gov/vocabulary/relators/aut$01017965 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483158003321 996 $aStatistics Based on Dirichlet Processes and Related Topics$92391166 997 $aUNINA