Keywords: MCEM algorithm; Gibbs sampler; Multivariate probit model; Multi-group; BIC. / The main purpose of this paper is to develop maximum likelihood and Bayesian approach for the multivariate probit model in several populations. A Monte Carlo EM algorithm is proposed for obtaining the maximum likelihood estimates and the Gibbs sampler is used to produce the joint Bayesian estimates. To test hypotheses involving constraints among the structural parameters of MP model across groups, we use the method of Bayesian Information Criterion(BIC). The simulation study will be given to certify the accuracy of our algorithm. / Yu, Yin. / "March 2007." / Adviser: Sik Yum Lee. / Source: Dissertation Abstracts International, Volume: 68-09, Section: B, page: 6054. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 135-137). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

by Hing-cheung So. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 133-141). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Time Delay Estimation (TDE) and its Applications --- p.1 / Chapter 1.2 --- Goal of the Work --- p.6 / Chapter 1.3 --- Thesis Outline --- p.9 / Chapter 2 --- Adaptive Methods for TDE --- p.10 / Chapter 2.1 --- Problem Description --- p.11 / Chapter 2.2 --- The Least Mean Square Time Delay Estimator (LMSTDE) --- p.11 / Chapter 2.2.1 --- Bias and Variance --- p.14 / Chapter 2.2.2 --- Probability of Occurrence of False Peak Weight --- p.16 / Chapter 2.2.3 --- Some Modifications of the LMSTDE --- p.17 / Chapter 2.3 --- The Adaptive Digital Delay-Lock Discriminator (ADDLD) --- p.18 / Chapter 2.4 --- Summary --- p.20 / Chapter 3 --- The Explicit Time Delay Estimator (ETDE) --- p.22 / Chapter 3.1 --- Derivation and Analysis of the ETDE --- p.23 / Chapter 3.1.1 --- The ETDE system --- p.23 / Chapter 3.1.2 --- Performance Surface --- p.26 / Chapter 3.1.3 --- Static Behaviour --- p.28 / Chapter 3.1.4 --- Dynamic Behaviour --- p.30 / Chapter 3.2 --- Performance Comparisons --- p.32 / Chapter 3.2.1 --- With the LMSTDE --- p.32 / Chapter 3.2.2 --- With the CATDE --- p.34 / Chapter 3.2.3 --- With the CRLB --- p.35 / Chapter 3.3 --- Simulation Results --- p.38 / Chapter 3.3.1 --- Corroboration of the ETDE Performance --- p.38 / Chapter 3.3.2 --- Comparative Studies --- p.44 / Chapter 3.4 --- Summary --- p.48 / Chapter 4 --- An Improvement to the ETDE --- p.49 / Chapter 4.1 --- Delay Modeling Error of the ETDE --- p.49 / Chapter 4.2 --- The Explicit Time Delay and Gain Estimator (ETDGE) --- p.52 / Chapter 4.3 --- Performance Analysis --- p.55 / Chapter 4.4 --- Simulation Results --- p.57 / Chapter 4.5 --- Summary --- p.61 / Chapter 5 --- TDE in the Presence of Multipath Propagation --- p.62 / Chapter 5.1 --- The Multipath TDE problem --- p.63 / Chapter 5.2 --- TDE with Multipath Cancellation (MCTDE) --- p.64 / Chapter 5.2.1 --- Structure and Algorithm --- p.64 / Chapter 5.2.2 --- Convergence Dynamics --- p.67 / Chapter 5.2.3 --- The Generalized Multipath Cancellator --- p.70 / Chapter 5.2.4 --- Effects of Additive Noises --- p.73 / Chapter 5.2.5 --- Simulation Results --- p.74 / Chapter 5.3 --- TDE with Multipath Equalization (METDE) --- p.86 / Chapter 5.3.1 --- The Two-Step Algorithm --- p.86 / Chapter 5.3.2 --- Performance of the METDE --- p.89 / Chapter 5.3.3 --- Simulation Results --- p.93 / Chapter 5.4 --- Summary --- p.101 / Chapter 6 --- Conclusions and Suggestions for Future Research --- p.102 / Chapter 6.1 --- Conclusions --- p.102 / Chapter 6.2 --- Suggestions for Future Research --- p.104 / Appendices --- p.106 / Chapter A --- Derivation of (3.20) --- p.106 / Chapter B --- Derivation of (3.29) --- p.110 / Chapter C --- Derivation of (4.14) --- p.111 / Chapter D --- Derivation of (4.15) --- p.113 / Chapter E --- Derivation of (5.21) --- p.115 / Chapter F --- Proof of unstablity of A°(z) --- p.116 / Chapter G --- Derivation of (5.34)-(5.35) --- p.118 / Chapter H --- Derivation of variance of αs11(k) and Δs11(k) --- p.120 / Chapter I --- Derivation of (5.40) --- p.123 / Chapter J --- Derivation of time constant of αΔ11(k) --- p.124 / Chapter K --- Derivation of (5.63)-(5.66) --- p.125 / Chapter L --- Derivation of (5.68)-(5.72) --- p.129 / References --- p.133

by Lo Tai-yan, Milton. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 112-114). / Chapter 1 --- Preliminaries --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.1.1 --- The Noncentral Multivariate F distribution --- p.2 / Chapter 1.1.2 --- The Central Problems and the Approach --- p.4 / Chapter 1.2 --- Concepts and Terminology --- p.7 / Chapter 1.3 --- Choice of Estimates --- p.10 / Chapter 1.4 --- Related Work --- p.11 / Chapter 2 --- Estimation of the noncentrality parameter of a Noncentral Mul- tivariate F distribution --- p.19 / Chapter 2.1 --- Unbiased and Linear Estimators --- p.19 / Chapter 2.1.1 --- The unbiased estimate --- p.20 / Chapter 2.1.2 --- The Class of Linear Estimates --- p.24 / Chapter 2.2 --- Optimal Linear Estimate --- p.32 / Chapter 2.3 --- Nonlinear Estimate --- p.34 / Chapter 2.4 --- Monte Carlo Simulation Study --- p.41 / Chapter 2.5 --- Evaluation and Further Investigation --- p.42 / Chapter 3 --- Estimation of Canonical Correlation Coefficients --- p.73 / Chapter 3.1 --- Preliminary --- p.73 / Chapter 3.2 --- The Estimation Problem --- p.76 / Chapter 3.3 --- Orthogonally Invariant Estimates --- p.77 / Chapter 3.3.1 --- The Unbiased Estimate --- p.78 / Chapter 3.3.2 --- The Class of Linear Estimates --- p.78 / Chapter 3.3.3 --- The Class of Nonlinear Estimates --- p.80 / Chapter 3.4 --- Monte Carlo Simulation Study --- p.87 / Chapter 3.5 --- Evaluation and Further Investigation --- p.89 / Chapter A --- p.104 / Chapter A.1 --- Lemma 3.2 --- p.104 / Chapter A.2 --- Theorem 3.3 Leung(1992) --- p.105 / Chapter A.3 --- The Noncentral F Identity --- p.106 / Chapter B --- Bibliography --- p.111

Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaf 34.

Leung Kit Ying. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 86-88). / Abstracts in English and Chinese. / Declaration --- p.i / Acknowledgement --- p.ii / Chapter 1 --- INTRODUCTION --- p.1 / Chapter 2 --- IMPROVED ESTIMATION OF THE NORMAL PRECISION MATRIX USING THE L1 AND L2 LOSS FUNCTIONS --- p.7 / Chapter 2.1 --- Previous Work --- p.9 / Chapter 2.2 --- Important Lemmas --- p.13 / Chapter 2.3 --- Improved Estimation of Σ-1 under L1 Loss Function --- p.20 / Chapter 2.4 --- Improved Estimation of Σ-1 under L2 Loss Function --- p.26 / Chapter 2.5 --- Simulation Study --- p.31 / Chapter 2.6 --- Comparison with Krishnammorthy and Gupta's result --- p.38 / Chapter 3 --- IMPROVED ESTIMATION OF THE NORMAL PRECISION MATRIX USING THE L3 AND L4 LOSS FUNCTIONS --- p.43 / Chapter 3.1 --- Justification of the Loss Functions --- p.46 / Chapter 3.2 --- Important Lemmas for Calculating Risks --- p.48 / Chapter 3.3 --- Improved Estimation of Σ-1 under L3 Loss Function --- p.55 / Chapter 3.4 --- Improved Estimation of Σ-1 under L4 Loss Function --- p.62 / Chapter 3.5 --- Simulation Study --- p.69 / Appendix --- p.77 / Reference --- p.35

Lam Yuk Hing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 67-70). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Diagnostic Measure --- p.7 / Chapter 2.1 --- A diagnostic measure di based on Cook's likelihood distance --- p.7 / Chapter 2.2 --- The estimates 6 and θ (i) --- p.8 / Chapter 2.3 --- "The one-step estimator,θ1 (i)" --- p.9 / Chapter 3 --- Methods For Identifying Influential Observations --- p.11 / Chapter 3.1 --- One-step method --- p.11 / Chapter 3.2 --- Forward search procedure --- p.13 / Chapter 3.2.1 --- Idea of forward search procedure --- p.14 / Chapter 3.2.2 --- "The modified diagnostic measure, di" --- p.15 / Chapter 3.2.3 --- Initial basic subset --- p.18 / Chapter 3.2.4 --- The algorithm of starting with an ordered basic subset --- p.19 / Chapter 3.2.5 --- The algorithm of starting with a random basic subset --- p.21 / Chapter 4 --- Case Study --- p.23 / Chapter 4.1 --- Open/Close Book data set --- p.23 / Chapter 4.1.1 --- One-step method --- p.27 / Chapter 4.1.2 --- Forward search procedure --- p.28 / Chapter 4.1.3 --- Start with the ordered basic subset --- p.28 / Chapter 4.1.4 --- Start with a random basic subset --- p.32 / Chapter 4.2 --- Paper-Quality Measurements data set --- p.38 / Chapter 4.2.1 --- One-step method --- p.40 / Chapter 4.2.2 --- Forward search procedure --- p.41 / Chapter 4.2.3 --- Start with the ordered basic subset --- p.41 / Chapter 4.2.4 --- Start with a random basic subset --- p.45 / Chapter 5 --- Simulation --- p.52 / Chapter 5.1 --- Simulation procedure --- p.52 / Chapter 5.2 --- Results --- p.56 / Chapter 6 --- Discussion --- p.64 / Reference --- p.67

Chau Ka Pik. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 39-40). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Maximum Probability Estimator --- p.1 / Chapter 1.2 --- An Outline of the Thesis --- p.4 / Chapter 2 --- Asymptotic Distribution Theory --- p.7 / Chapter 3 --- Exponential Family Noise --- p.16 / Chapter 3.1 --- Stationary Case --- p.16 / Chapter 3.2 --- Nonstationary Case --- p.25 / Chapter 4 --- Conclusions --- p.37 / Bibliography --- p.39

by Yuen Wai-ying. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 50-51). / Abstract also in Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Estimation of Factor Scores in a Three-level Factor Analysis Model / Chapter 2.1 --- The Three-level Factor Analysis Model --- p.5 / Chapter 2.2 --- Estimation of Factor Scores in Between-group --- p.7 / Chapter 2.2.1 --- REG Method --- p.9 / Chapter 2.2.2 --- GLS Method --- p.11 / Chapter 2.3 --- Estimation of Factor Scores in Second Level Within-group --- p.13 / Chapter 2.3.1 --- REG Method --- p.15 / Chapter 2.3.2 --- GLS Method --- p.17 / Chapter 2.4 --- Estimation of Factor Scores in First Level Within-group / Chapter 2.4.1 --- First Approach --- p.19 / Chapter 2.4.2 --- Second Approach --- p.24 / Chapter 2.4.3 --- Comparison of the Two Approaches in Estimating Factor Scores in First Level Within-group --- p.31 / Chapter 2.5 --- Summary on the REG and GLS Methods --- p.35 / Chapter Chapter 3 --- Simulation Studies / Example1 --- p.37 / Example2 --- p.42 / Chapter Chapter 4 --- Conclusion and Discussion --- p.48 / References --- p.50 / Figures --- p.52

潜变量模型作为处理多元数据的一种有效的方法，在行为学、教育学、社会心理学以及医学等各个领域都受到了广泛关注。在分析潜变量模型时，大多数现有的统计方法和软件都是基于响应变量为正态分布的假设。尽管一些最近发展的方法可以处理部分的非正态数据，但在分析高度非正态的数据时依然存在问题。此外，在实际研究中还经常会遇到不完全数据，如缺失数据和删失数据。简单地忽略或错误地处理不完全数据可能会严重扭曲统计结果。在本文中，我们发展了贝叶斯惩罚样条方法，同时采用马尔科夫链蒙特卡洛方法，用以分析存有高度非正态和不完全数据的变换潜变量模型。我们在变换潜变量模型中讨论了不同类型的不完全数据，如完全随机缺失数据、随机缺失数据、不可忽略的缺失数据以及删失数据。我们还利用离差信息准则来选择正确的模型和数据缺失机制。我们通过许多模拟研究论证了我们提出的方法。此方法被应用于关于工作满意度、家庭生活、工作态度的研究，以及香港地区2 型糖尿病患者心血管疾病的研究。 / Latent variable models (LVMs), as useful multivariate techniques, have attracted significant attention from various fields, including the behavioral, educational, social-psychological, and medical sciences. In the analysis of LVMs, most existing statistical methods and software have been developed under the normal assumption of response variables. While some recent developments can partially address the non-normality of data, they are still problematic in dealing with highly non-normal data. Moreover, the presence of incomplete data, such as missing data and censoring data, is a practical issue in substantive research. Simply ignoring incomplete data or wrongly managing incomplete data might seriously distort statistical influence results. In this thesis, we develop a Bayesian P-spline approach, coupled with Markov chain Monte Carlo (MCMC) methods, to analyze transformation LVMs with highly non-normal and incomplete data. Different types of incomplete data, such as missing completely at random data, missing at random data, nonignorable missing data, as well as censored data, are discussed in the context of transformation LVMs. The deviance information criterion is proposed to conduct model comparison and select an appropriate missing mechanism. The empirical performance of the proposed methodologies is examined via many simulation studies. Applications to a study concerning people's job satisfaction, home life, and work attitude, as well as a study on cardiovascular diseases for type 2 diabetic patients in Hong Kong are presented. / Detailed summary in vernacular field only. / Liu, Pengfei. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 115-127). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.ii / Acknowledgement --- p.v / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Latent Variable Models --- p.1 / Chapter 1.2 --- Missing Data --- p.4 / Chapter 1.3 --- Censoring Data --- p.5 / Chapter 1.4 --- Penalized B-splines --- p.6 / Chapter 1.5 --- Bayesian Methods --- p.7 / Chapter 1.6 --- Outline of the Thesis --- p.8 / Chapter 2 --- Transformation Structural Equation Models --- p.9 / Chapter 2.1 --- Introduction --- p.9 / Chapter 2.2 --- Model Description --- p.11 / Chapter 2.3 --- Bayesian Estimation --- p.12 / Chapter 2.3.1 --- Bayesian P-splines --- p.12 / Chapter 2.3.2 --- Identifiability Constraints --- p.15 / Chapter 2.3.3 --- Prior Distributions --- p.16 / Chapter 2.3.4 --- Posterior Inference --- p.18 / Chapter 2.4 --- Bayesian Model Selection via DIC --- p.20 / Chapter 2.5 --- Simulation Studies --- p.23 / Chapter 2.5.1 --- Simulation 1 --- p.23 / Chapter 2.5.2 --- Simulation 2 --- p.26 / Chapter 2.5.3 --- Simulation 3 --- p.27 / Chapter 2.6 --- Conclusion --- p.28 / Chapter 3 --- Transformation SEMs with Missing Data that are Missing At Random --- p.43 / Chapter 3.1 --- Introduction --- p.43 / Chapter 3.2 --- Model Description --- p.45 / Chapter 3.3 --- Bayesian Estimation and Model Selection --- p.46 / Chapter 3.3.1 --- Modeling Transformation Functions --- p.46 / Chapter 3.3.2 --- Identifiability Constraints --- p.47 / Chapter 3.3.3 --- Prior Distributions --- p.48 / Chapter 3.3.4 --- Bayesian Estimation --- p.49 / Chapter 3.3.5 --- Model Selection via DIC --- p.52 / Chapter 3.4 --- Simulation Studies --- p.53 / Chapter 3.4.1 --- Simulation 1 --- p.54 / Chapter 3.4.2 --- Simulation 2 --- p.56 / Chapter 3.5 --- Conclusion --- p.57 / Chapter 4 --- Transformation SEMs with Nonignorable Missing Data --- p.65 / Chapter 4.1 --- Introduction --- p.65 / Chapter 4.2 --- Model Description --- p.67 / Chapter 4.3 --- Bayesian Inference --- p.68 / Chapter 4.3.1 --- Model Identification and Prior Distributions --- p.68 / Chapter 4.3.2 --- Posterior Inference --- p.69 / Chapter 4.4 --- Selection of Missing Mechanisms --- p.71 / Chapter 4.5 --- Simulation studies --- p.73 / Chapter 4.5.1 --- Simulation 1 --- p.73 / Chapter 4.5.2 --- Simulation 2 --- p.76 / Chapter 4.6 --- A Real Example --- p.77 / Chapter 4.7 --- Conclusion --- p.79 / Chapter 5 --- Transformation Latent Variable Models with Multivariate Censored Data --- p.86 / Chapter 5.1 --- Introduction --- p.86 / Chapter 5.2 --- Model Description --- p.88 / Chapter 5.3 --- Bayesian Inference --- p.90 / Chapter 5.3.1 --- Model Identification and Bayesian P-splines --- p.90 / Chapter 5.3.2 --- Prior Distributions --- p.91 / Chapter 5.3.3 --- Posterior Inference --- p.93 / Chapter 5.4 --- Simulation Studies --- p.96 / Chapter 5.4.1 --- Simulation 1 --- p.96 / Chapter 5.4.2 --- Simulation 2 --- p.99 / Chapter 5.5 --- A Real Example --- p.100 / Chapter 5.6 --- Conclusion --- p.103 / Chapter 6 --- Conclusion and Further Development --- p.113 / Bibliography --- p.115

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Lawrence Charles Vallot. / M.S.