by Shiu-kwok Lau. / Bibliography: leaves 41-43 / Thesis (M.Ph.)--Chinese University of Hong Kong, 1985

Siu-man Ng. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaves 44-47.

by Ming-long Lam. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaves 41-43.

by Terry Shing-fong Lew. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 40-42). / Chapter Chapter 1 --- Introduction --- p.Page1 / Chapter Chapter 2 --- Measures of Association for Polytomous Variables --- p.Page5 / Chapter §2.1 --- "Notations," --- p.5 / Chapter §2.2 --- "Pearson Product-moment Correlation Coefficient," --- p.6 / Chapter §2.3 --- "Spearman Rank Correlation Coefficient," --- p.7 / Chapter §2.4 --- "Kendall's Tau-b," --- p.9 / Chapter §2.5 --- "Polychoric Correlation Coefficient," --- p.9 / Chapter Chapter 3 --- Monte Carlo Study of Measures of Association for Polytomous Variables with Multivariate Normal Distribution --- p.Page 13 / Chapter §3.1 --- "Design," --- p.13 / Chapter §3.2 --- "Results and Findings," --- p.18 / Chapter §3.3 --- "Discussion," --- p.23 / Chapter §3.4 --- "Implications," --- p.26 / Chapter Chapter 4 --- Monte Carlo Studies for Polytomous Variables with Non-normal Distribution --- p.Page 27 / Chapter §4.1 --- "Elliptica1-t Distribution," --- p.27 / Chapter §4.2 --- "Design," --- p.28 / Chapter §4.3 --- "Results and Findings," --- p.30 / Chapter §4.4 --- "Discussion," --- p.33 / Chapter §4.5 --- "Implications," --- p.34 / Chapter Chapter 5 --- Conclusion --- p.Page36 / References --- p.Page40 / Figures --- p.Page43 / Tables --- p.Page51

by Mannon Wong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 42-47). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Maximum Likelihood Estimations of Polyserial Correlations --- p.7 / Chapter 3 --- Normal Curvature and the Conformal Normal Curvature of Lo- cal Influence --- p.12 / Chapter 3.1 --- Normal Curvature --- p.14 / Chapter 3.2 --- Conformal Normal Curvature as an Influential Measure --- p.16 / Chapter 4 --- Influential Observations in the Estimations of Polyserial Corre- lations and the Thresholds --- p.18 / Chapter 4.1 --- Case-weights perturbation --- p.18 / Chapter 4.2 --- "Observations Influencing the Estimates of = (μ, Σ, ε，T)" --- p.20 / Chapter 4.3 --- "Observations Influencing the Estimates of θ1 = （(μ, Σ)" --- p.25 / Chapter 4.4 --- Observations Influencing the Estimates of θ2 = （(ε，T) --- p.27 / Chapter 5 --- Examples --- p.28 / Chapter 5.1 --- Cox's Data --- p.28 / Chapter 5.2 --- Aids Data --- p.32 / Chapter 5.3 --- Simulation Data --- p.35 / Chapter 6 --- Discussion --- p.38 / Chapter 7 --- References --- p.42 / Chapter A --- Appendix I --- p.48 / Chapter B --- Appendix II --- p.50 / Chapter C --- Appendix III --- p.73

Yiu Choi Fan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 69-71). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Estimation with Known Misclassification Probabilities --- p.7 / Chapter 2.1 --- Model --- p.7 / Chapter 2.2 --- Maximum Likelihood Estimation --- p.9 / Chapter 2.3 --- Standard Errors of the Parameter Estimates --- p.12 / Chapter 3 --- Numerical Examples (I) --- p.13 / Chapter 3.1 --- Analysis of Real Data --- p.13 / Chapter 3.2 --- Analysis of Artificial Data --- p.16 / Chapter 4 --- Simulation Study (I) --- p.19 / Chapter 4.1 --- Simulation Algorithm --- p.19 / Chapter 4.2 --- Simulation Design --- p.20 / Chapter 4.3 --- Reported Statistics --- p.21 / Chapter 4.4 --- Conclusions of Simulation Results --- p.22 / Chapter 5 --- Estimation by Double Sampling Scheme --- p.24 / Chapter 5.1 --- Introduction of Double Sampling Scheme --- p.24 / Chapter 5.2 --- Model --- p.25 / Chapter 5.3 --- Minimum Chi-square Estimation --- p.26 / Chapter 5.4 --- Statistical Properties of the Parameter Estimates --- p.28 / Chapter 6 --- Numerical Examples (II) --- p.30 / Chapter 6.1 --- "Analysis of Real Data, (2x2 Table)" --- p.30 / Chapter 6.2 --- Analysis of Artificial Data (3x3 Table) --- p.32 / Chapter 7 --- Simulation Study (II) --- p.34 / Chapter 7.1 --- Simulation Algorithm --- p.34 / Chapter 7.2 --- Simulation Design --- p.35 / Chapter 7.3 --- Reported Statistics --- p.37 / Chapter 7.4 --- Conclusions of Simulation Results --- p.38 / Chapter 8 --- Conclusions --- p.39 / Appendices --- p.42 / Chapter A.1 --- The proof of the expression for P(Zj = Ehk) --- p.42 / Chapter A.2 --- The proof of puv and whk{uv) --- p.44 / Chapter A.3 --- The proof of the covariance matrix Q --- p.47 / Chapter A.4 --- The proof of the matrix Σ --- p.52 / Tables A1-A9 --- p.54 / Tables B1-B6 --- p.63 / Bibliography --- p.69

A modelagem de equações estruturais é uma técnica estatística multivariada que permite analisar variáveis que não podem ser medidas diretamente, mas que podem ser estimadas através de indicadores. Dado o poder que esta técnica tem em acomodar diversas situações em um único modelo, sua aplicação vem crescendo nas diversas áreas do conhecimento. Diante disto, este trabalho teve por objetivo avaliar a incorporação de indicadores categóricos ordinais em modelos de equações estruturais, fazendo um resumo dos principais procedimentos teóricos e subjetivos presentes no processo de estimação de um modelo, avaliando as suposições violadas quando indicadores ordinais são utilizados para estimar variáveis latentes e criando diretrizes que devem ser seguidas para a correta estimação dos parâmetros do modelo. Mostramos que as correlações especiais (correlação tetracórica, correlação policórica, correlação biserial e correlação poliserial) são as melhores escolhas como medida de associação entre indicadores, que estimam com maior precisão a correlação entre duas variáveis, em comparação à correlação de Pearson, e que são robustas a desvios de simetria e curtose. Por fim aplicamos os conceitos apresentados ao longo deste estudo a dois modelos hipotéticos com o objetivo de avaliar as diferenças entre os parâmetros estimados quando um modelo é ajustado utilizando a matriz de correlações especiais em substituição à matriz de correlação de Pearson. / The structural equation modeling is a multivariate statistical technique that allows us to analyze variables that cant be measured directly but can be estimated through indicators. Given the power that this technique has to accommodate several situations in a single model, its application has increased in several areas of the knowledge. At first, this study aimed to evaluate the incorporation of ordinal categorical indicators in structural equation models, making a summary of the major theoretical and subjective procedures of estimating the present model, assessing the assumptions that are violated when ordinal indicators are used to estimate latent variables and creating guidelines to be followed to correct estimation of model parameters. We show that the special correlations (tetrachoric correlation, polychoric correlation, biserial correlation and poliserial correlation) are the best choices as a measure of association between indicators, that estimate more accurately the correlation between two variables, compared to Pearsons correlation, and that they are robust to deviations from symmetry and kurtosis. Finally, we apply the concepts presented in this study to two hypothetical models to evaluate the differences between the estimated parameters when a model is adjusted using the special correlation matrix substituting the Pearsons correlation matrix.

Ho, Yuk Kwan = 粒子鏈的布朗運動 : 相互關係時間之探討 / 何煜坤. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 82-84). / Abstracts in English and Chinese. / Ho, Yuk Kwan = Li zi lian de Bulang yun dong : xiang hu guan xi shi jian zhi tan tao / He Yukun. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Historical background --- p.1 / Chapter 1.2 --- Motivation --- p.4 / Chapter 2 --- Modelling of the system of the particle chain --- p.6 / Chapter 2.1 --- Interactions between the particles --- p.7 / Chapter 2.2 --- Assumptions of the Brownian force --- p.10 / Chapter 3 --- Time evolution of the probability distribution --- p.14 / Chapter 3.1 --- Diffusion under a uniform external force field --- p.14 / Chapter 3.2 --- Multi-dimensional Fokker-Planck equation --- p.18 / Chapter 3.3 --- Fundamental solution to the Fokker-Planck equation --- p.21 / Chapter 3.3.1 --- Fulfillment of the Fokker-Planck equation by the stochas- tic process described by the Langevin equation --- p.21 / Chapter 3.3.2 --- Gaussian process of the stochastic process in the system --- p.24 / Chapter 3.4 --- Relaxation of the fluctuations and the variances of the system --- p.27 / Chapter 3.4.1 --- Dependence of system parameters - study of a two-body system --- p.27 / Chapter 3.4.2 --- Dependence of system size --- p.33 / Chapter 4 --- Time evolution of the correlation function --- p.36 / Chapter 4.1 --- Method of Rice - harmonic analysis --- p.38 / Chapter 4.1.1 --- Natural mode expansion of the correlation functions --- p.41 / Chapter 4.1.2 --- Satisfaction of the equipartition principle --- p.44 / Chapter 4.2 --- Relaxation of the correlation functions --- p.45 / Chapter 4.2.1 --- Dependence of system parameters - study of a two body system --- p.46 / Chapter 4.2.2 --- Dependence of system size --- p.50 / Chapter 4.3 --- Connection with relaxation modes of fluctuations and variances --- p.53 / Chapter 5 --- Coloured Brownian force --- p.58 / Chapter 5.1 --- Fluctuation-dissipation theorem --- p.59 / Chapter 5.2 --- The system of a large particle with a particle chain --- p.64 / Chapter 5.2.1 --- Equivalent heat bath with which the large particleis interacting --- p.67 / Chapter 5.2.2 --- Retarded friction from its underlying physical origin --- p.71 / Chapter 5.2.3 --- Effective random force of the heat bath and its underly- ing physical origin --- p.73 / Chapter 5.2.4 --- Displacement correlation function for the large particle interacting with the heat bath --- p.77 / Chapter 6 --- Conclusion --- p.81 / Bibliography --- p.82 / Chapter A --- Magnetic force between two magnetic dipoles --- p.85 / Chapter B --- Hydrodynamic interaction --- p.88 / Chapter B.l --- Faxen´ةs Law --- p.90 / Chapter B.2 --- Method of reflection --- p.92 / Chapter B.3 --- Interactions between three translating identical spheres --- p.94 / Chapter C --- Proof of the cross-correlation theorem and Wiener-Kintchine theorem --- p.97 / Chapter D --- Proof of the relation between θ(t) and β(t) in Eq. 5.42 --- p.99 / Chapter E --- Proof of the zero-value of k in Eq. 5.60 --- p.101

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