by Long Mei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 73-77). / Abstracts in English and Chinese. / Acknowledgements --- p.iv / Abstract --- p.v / Table of Contents --- p.vii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Nonlinear Factor Analysis Model --- p.1 / Chapter 1.2 --- Main Objectives --- p.2 / Chapter 1.2.1 --- Investigation of the performance of the ML approach with MCECM algorithm in NFA model --- p.2 / Chapter 1.2.2 --- Investigation of the Robustness of the ML approach with MCECM algorithm --- p.3 / Chapter 1.3 --- Structure of the Thesis --- p.3 / Chapter 2 --- Theoretical Background of the MCECM Algorithm --- p.5 / Chapter 2.1 --- Introduction of the EM algorithm --- p.5 / Chapter 2.2 --- Monte Carlo integration --- p.7 / Chapter 2.3 --- Markov Chains --- p.7 / Chapter 2.4 --- The Metropolis-Hastings algorithm --- p.8 / Chapter 3 --- Maximum Likelihood Estimation of a Nonlinear Factor Analysis Model --- p.10 / Chapter 3.1 --- MCECM Algorithm --- p.10 / Chapter 3.1.1 --- Motivation of Using MCECM algorithm --- p.11 / Chapter 3.1.2 --- Introduction of the Realization of the MCECM algorithm --- p.12 / Chapter 3.1.3 --- Implementation of the E-step via the MH Algorithm --- p.13 / Chapter 3.1.4 --- Maximization Step --- p.15 / Chapter 3.2 --- Monitoring Convergence of MCECM --- p.17 / Chapter 3.2.1 --- Bridge Sampling Method --- p.17 / Chapter 3.2.2 --- Average Batch Mean Method --- p.18 / Chapter 4 --- Simulation Studies --- p.20 / Chapter 4.1 --- The First Simulation Study with the Normal Distribution --- p.20 / Chapter 4.1.1 --- Model Specification --- p.20 / Chapter 4.1.2 --- The Selection of System Parameters --- p.22 / Chapter 4.1.3 --- Monitoring the Convergence --- p.22 / Chapter 4.1.4 --- Simulation Results for the ML Estimates --- p.25 / Chapter 4.2 --- The Second Simulation Study with the Normal Distribution --- p.34 / Chapter 4.2.1 --- Model Specification --- p.34 / Chapter 4.2.2 --- Monitoring the Convergence --- p.35 / Chapter 4.2.3 --- Simulation Results for the ML Estimates --- p.38 / Chapter 4.3 --- The Third Simulation Study on Robustness --- p.47 / Chapter 4.3.1 --- Model Specification --- p.47 / Chapter 4.3.2 --- Monitoring the Convergence --- p.48 / Chapter 4.3.3 --- Simulation Results for the ML Estimates --- p.51 / Chapter 4.4 --- The Fourth Simulation Study on Robustness --- p.59 / Chapter 4.4.1 --- Model Specification --- p.59 / Chapter 4.4.2 --- Monitoring the Convergence --- p.59 / Chapter 4.4.3 --- Simulation Results for the ML Estimates --- p.62 / Chapter 5 --- Conclusion --- p.71 / Bibliography --- p.73
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_325258 |
| Date | January 2005 |
| Contributors | Long, Mei., Chinese University of Hong Kong Graduate School. Division of Statistics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, viii, 77 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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