On the rate of convergence of the ECME algorithm
This paper deals with the matrix rate of convergence of the ECME algorithm, a simple extention of EM and ECM algorithms proposed recently by Liu and Rubin. We establish a general formula for the matrix rate of convergence of ECME which is a generalization of the result of Liu and Rubin.
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| Published in | Statistics & probability letters Vol. 37; no. 1; pp. 81 - 87 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
15.01.1998
Elsevier |
| Series | Statistics & Probability Letters |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0167-7152 1879-2103 |
| DOI | 10.1016/S0167-7152(97)00103-X |
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| Abstract | This paper deals with the matrix rate of convergence of the ECME algorithm, a simple extention of EM and ECM algorithms proposed recently by Liu and Rubin. We establish a general formula for the matrix rate of convergence of ECME which is a generalization of the result of Liu and Rubin. |
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| AbstractList | This paper deals with the matrix rate of convergence of the ECME algorithm, a simple extention of EM and ECM algorithms proposed recently by Liu and Rubin. We establish a general formula for the matrix rate of convergence of ECME which is a generalization of the result of Liu and Rubin. |
| Author | Mkhadri, Abdallah |
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| Keywords | Missing data Incomplete data ECM algorithm Rate of convergence EM algorithm ECME algorithm Convergence rate Data analysis Incomplete information |
| Language | English |
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| References | Meng (BIB6) 1994; 22 Liu, Rubin (BIB4) 1994; 81 Meng, Rubin (BIB5) 1993; 80 Dempster, Laird, Rubin (BIB3) 1977; 39 Meng, van Dyk (BIB7) 1997 Davis (BIB2) 1965; vol. 55 Besag (BIB1) 1986; 48 Meng (10.1016/S0167-7152(97)00103-X_BIB7) 1997 Liu (10.1016/S0167-7152(97)00103-X_BIB4) 1994; 81 Meng (10.1016/S0167-7152(97)00103-X_BIB5) 1993; 80 Meng (10.1016/S0167-7152(97)00103-X_BIB6) 1994; 22 Dempster (10.1016/S0167-7152(97)00103-X_BIB3) 1977; 39 Davis (10.1016/S0167-7152(97)00103-X_BIB2) 1965; vol. 55 Besag (10.1016/S0167-7152(97)00103-X_BIB1) 1986; 48 |
| References_xml | – volume: vol. 55 start-page: 253 year: 1965 end-page: 294 ident: BIB2 article-title: Gamma function and related functions publication-title: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Applied Mathematics Series – volume: 80 start-page: 267 year: 1993 end-page: 278 ident: BIB5 article-title: Maximum likelihood estimation via the ECM algorithm: A general framework publication-title: Biometrika – volume: 48 start-page: 259 year: 1986 end-page: 302 ident: BIB1 article-title: On the statistical analysis of dirty pictures (with discussion) publication-title: J. R. Statist. Soc. B – year: 1997 ident: BIB7 article-title: The EM algorithm — An old folk song sung to a fast new tune publication-title: J. Roy. Statist. Soc. B – volume: 81 start-page: 633 year: 1994 end-page: 648 ident: BIB4 article-title: The ECME algorithm: a simple extension of EM and ECM with faster monotone convergence publication-title: Biometrika – volume: 39 start-page: 1 year: 1977 end-page: 38 ident: BIB3 article-title: Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion) publication-title: J. R. Statist. Soc. B – volume: 22 start-page: 326 year: 1994 end-page: 339 ident: BIB6 article-title: On the rate of convergence of the ECM algorithm publication-title: Ann. Statist. – volume: vol. 55 start-page: 253 year: 1965 ident: 10.1016/S0167-7152(97)00103-X_BIB2 article-title: Gamma function and related functions – volume: 22 start-page: 326 year: 1994 ident: 10.1016/S0167-7152(97)00103-X_BIB6 article-title: On the rate of convergence of the ECM algorithm publication-title: Ann. Statist. doi: 10.1214/aos/1176325371 – volume: 39 start-page: 1 year: 1977 ident: 10.1016/S0167-7152(97)00103-X_BIB3 article-title: Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion) publication-title: J. R. Statist. Soc. B doi: 10.1111/j.2517-6161.1977.tb01600.x – year: 1997 ident: 10.1016/S0167-7152(97)00103-X_BIB7 article-title: The EM algorithm — An old folk song sung to a fast new tune publication-title: J. Roy. Statist. Soc. B doi: 10.1111/1467-9868.00082 – volume: 80 start-page: 267 year: 1993 ident: 10.1016/S0167-7152(97)00103-X_BIB5 article-title: Maximum likelihood estimation via the ECM algorithm: A general framework publication-title: Biometrika doi: 10.1093/biomet/80.2.267 – volume: 81 start-page: 633 year: 1994 ident: 10.1016/S0167-7152(97)00103-X_BIB4 article-title: The ECME algorithm: a simple extension of EM and ECM with faster monotone convergence publication-title: Biometrika doi: 10.1093/biomet/81.4.633 – volume: 48 start-page: 259 year: 1986 ident: 10.1016/S0167-7152(97)00103-X_BIB1 article-title: On the statistical analysis of dirty pictures (with discussion) publication-title: J. R. Statist. Soc. B doi: 10.1111/j.2517-6161.1986.tb01412.x |
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| SubjectTerms | ECM algorithm ECME algorithm EM algorithm Exact sciences and technology Incomplete data Incomplete data Missing data EM algorithm ECM algorithm ECME algorithm Rate of convergence Mathematics Missing data Multivariate analysis Probability and statistics Rate of convergence Sciences and techniques of general use Statistics |
| Title | On the rate of convergence of the ECME algorithm |
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