Thesis (Ph. D.)--University of Hawaii at Manoa, 1998. / Includes bibliographical references (leaves 116-119). Also available by subscription via the World Wide Web.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2002. / Includes bibliographical references (leaves 35-36). Also available in electronic version. Access restricted to campus users.

The problem of this study was to seek a goodness-of-fit index to compare covariance structure matrices based on the distribution of the mean of the logarithms of the eigenvalues.

The study seeks to determine the robustness and power of parametric analysis of covariance and analysis of covariance using rank transformation to violation of the assumption of normality. The study employs a Monte Carlo simulation procedure with varying conditions of population distribution, group size, equality of group size, scale length, regression slope, and Y-intercept. The procedure was performed on raw data and ranked data with untied ranks and tied ranks.

Shu-jia Wang. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 94-101). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Estimation of Structural Equation Models --- p.7 / Chapter Chapter 3 --- Statistical Curvatures in Structural Equation Models --- p.11 / Chapter 3.1 --- The Intrinsic and Parameter-effects Curvatures --- p.12 / Chapter 3.2 --- The Three Dimensional Curvature Arrays --- p.16 / Chapter Chapter 4 --- Bias and Covariance Matrix of the GLS Estimates --- p.20 / Chapter 4.1 --- Stochastic Expansion of the GLS Estimates --- p.20 / Chapter 4.2 --- The Second Order Approximation of the Bias --- p.23 / Chapter 4.3 --- The Second Order Approximation of Covariance Matrix of the GLS Estimates --- p.25 / Chapter 4.4 --- An Artificial Example --- p.29 / Chapter 4.5 --- Discussion --- p.33 / Chapter Chapter 5 --- Information Loss of the Estimators Under Assumption of Multivariate Normality --- p.35 / Chapter Chapter 6 --- Sensitivity Analysis of Structural Equation Models --- p.44 / Chapter 6.1 --- Introduction --- p.44 / Chapter 6.2 --- General Theory of Local Influence Analysisin Structural Equation Models --- p.46 / Chapter 6.3 --- Perturbation to the Case Weights in the GLS Estimation --- p.50 / Chapter 6.4 --- Cook's Distance in the Case Deletion Approach --- p.54 / Chapter 6.5 --- Relationship of Local Influence and Influence Function --- p.59 / Chapter 6.6 --- Illustrative Examples --- p.61 / Chapter 6.7 --- Sensitivity Analysis of Parameters --- p.63 / Chapter 6.8 --- Discussion --- p.68 / Chapter Chapter 7 --- Sensitivity Analysis of Structural Equation Models with Equality Functional Constraints --- p.70 / Chapter 7.1 --- Introduction --- p.70 / Chapter 7.2 --- Local Influence of Structural Equation Models With Constraints --- p.71 / Chapter 7.2.1 --- General Theory --- p.72 / Chapter 7.2.2 --- Perturbation to Case Weights in Constrained GLS Estimation --- p.77 / Chapter 7.2.3 --- Relationship of Local Influence and Influence Function --- p.79 / Chapter 7.3 --- Generalized Cook's Distance: Case Deletion Approach --- p.81 / Chapter 7.4 --- An Illustrative Example --- p.84 / Chapter 7.5 --- Sensitivity Analysis of Parameters With Constraints --- p.86 / Chapter 7.6 --- Discussion --- p.89 / Chapter Chapter 8 --- Summary and Discussion --- p.91 / References --- p.94 / Tables --- p.102 / Figures --- p.111

by Yin-Ping Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 95-96). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Estimation of the Correlation between Polytomous and Interval Data --- p.6 / Chapter 2.1 --- Model --- p.6 / Chapter 2.2 --- Maximum Likelihood Estimation --- p.8 / Chapter 2.3 --- Partition Maximum Likelihood Estimation --- p.10 / Chapter 2.4 --- Optimization Procedure and Simulation Study --- p.18 / Chapter Chapter 3 --- Three-stage Procedure for Covariance Structure Analysis --- p.25 / Chapter 3.1 --- Model --- p.25 / Chapter 3.2 --- Three-stage Estimation Method --- p.26 / Chapter 3.3 --- Optimization Procedure and Simulation Study --- p.38 / Chapter Chapter 4 --- Two-stage Procedure for Correlation Structure Analysis --- p.46 / Chapter 4.1 --- Model --- p.47 / Chapter 4.2 --- Two-stage Estimation Method --- p.47 / Chapter 4.3 --- Optimization Procedure and Monte Carlo Study --- p.50 / Chapter 4.4 --- Comparison of Two Methods --- p.53 / Chapter Chapter 5 --- Conclusion --- p.56 / Tables --- p.58 / References --- p.95

Modeling covariance structure is important for efficient estimation in longitudinal data models. Modified Cholesky decomposition (Pourahmadi, 1999) is used as an unconstrained reparameterization of the covariance matrix. The resulting new parameters have transparent statistical interpretations and are easily modeled using covariates. However, this approach is not directly applicable when the longitudinal data are unbalanced, because a Cholesky factorization for observed data that is coherent across all subjects usually does not exist. We overcome this difficulty by treating the problem as a missing data problem and employing a generalized EM algorithm to compute the ML estimators. We study the covariance matrices in both fixed-effects models and mixed-effects models for unbalanced longitudinal data. We illustrate our method by reanalyzing Kenwards (1987) cattle data and conducting simulation studies.

The first portion of this thesis develops efficient samplers for the Pólya-Gamma distribution, an essential component of the eponymous data augmentation technique that can be used to simulate posterior distributions derived from logistic likelihoods. Building fast computational schemes for such models is important due to their broad use across a range of disciplines, including economics, political science, epidemiology, ecology, psychology, and neuroscience. The second portion of this thesis explores models of time-varying covariance matrices for financial time series. Covariance matrices describe the dynamics of risk and the ability to forecast future variance and covariance has a direct impact on the investment decisions made by individuals, banks, funds, and governments. Two options are pursued. The first incorporates information from high-frequency statistics into factor stochastic volatility models while the second models high-frequency statistics directly. The performance of each is assessed based upon its ability to hedge risk within a class of similarly risky assets. / text

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2008. / Includes bibliographical references (leaves 148-150).

Thesis (Ph. D.)--University of Washington, 2008. / Vita. Includes bibliographical references (leaves 79-82).