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 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

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).

This thesis aims to develop some new and novel methods in advancing multivariate testing and multiple testing for high-dimensional small sample size data. In Chapter 2, we propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics under the assumption that the covariance matrices follow a diagonal matrix structure. In comparison with the diagonal Hotelling's tests, our proposed test statistics display some interesting characteristics. In particular, they are a summation of the log-transformed squared t-statistics rather than a direct summation of those components. More importantly, to derive the asymptotic normality of our test statistics under the null and local alternative hypotheses, we do not need the requirement that the covariance matrices follow a diagonal matrix structure. As a consequence, our proposed test methods are very flexible and readily applicable in practice. Monte Carlo simulations and a real data analysis are also carried out to demonstrate the advantages of the proposed methods. In Chapter 3, we propose a pairwise Hotelling's method for testing high-dimensional mean vectors. The new test statistics make a compromise on whether using all the correlations or completely abandoning them. To achieve the goal, we perform a screening procedure, pick up the paired covariates with strong correlations, and construct a classical Hotelling's statistic for each pair. While for the individual covariates without strong correlations with others, we apply squared t statistics to account for their respective contributions to the multivariate testing problem. As a consequence, our proposed test statistics involve a combination of the collected pairwise Hotelling's test statistics and squared t statistics. The asymptotic normality of our test statistics under the null and local alternative hypotheses are also derived under some regularity conditions. Numerical studies and two real data examples demonstrate the efficacy of our pairwise Hotelling's test. In Chapter 4, we propose a regularized t distribution and also explore its applications in multiple testing. The motivation of this topic dates back to microarray studies, where the expression levels of thousands of genes are measured simultaneously by the microarray technology. To identify genes that are differentially expressed between two or more groups, one needs to conduct hypothesis test for each gene. However, as microarray experiments are often with a small number of replicates, Student's t-tests using the sample means and standard deviations may suffer a low power for detecting differentially expressed genes. To overcome this problem, we first propose a regularized t distribution and derive its statistical properties including the probability density function and the moments. The noncentral regularized t distribution is also introduced for the power analysis. To demonstrate the usefulness of the proposed test, we apply the regularized t distribution to the gene expression detection problem. Simulation studies and two real data examples show that the regularized t-test outperforms the existing tests including Student's t-test and the Bayesian t-test in a wide range of settings, in particular when the sample size is small.

In structural equation models, researchers often examine two types of causal effects: direct and indirect effects. Direct effects involve variables that "directly" influence other variables, whereas indirect effects are transmitted via intervening variables. While researchers have paid considerable attention to the distribution of sample direct effects, the distribution of sample indirect effects has only recently been considered. Using the (delta) method (Rao, 1973), Sobel (1982) derived the asymptotic distribution for estimators of indirect effects in recursive systems. Sobel (1986) then derived the asymptotic distribution for estimators of total indirect effects in the Joreskog covariance structure model (Joreskog, 1977). This study examined the applicability of the large sample theory described by Sobel (1986) in small samples. Monte Carlo methods were used to evaluate the behavior of estimated total indirect effects in sample sizes of 50, 100, 200, 400, and 800. Two models were used in the analysis. Model 1 was a nonrecursive model with latent variables, feedback, and functional constraints among the effects (Duncan, Haller, & Portes, 1968; Sobel, 1986). Model 2 was a recursive model with observable variables (Duncan, Featherman, & Duncan, 1972). In addition, variations in these models were studied by randomly increasing and decreasing model parameters. The principal findings of the study suggest certain guidelines for researchers who use Sobel's procedures to evaluate total indirect effects in structural equation models. In order for the behavior of the estimates to approximate the asymptotic properties, sample sizes of 400 or more are indicated for nonrecursive systems similar to Model 1, and for recursive systems such as Model 2, sample sizes of 200 or more are suggested. At these sample sizes, researchers can expect sample indirect effects to be accurate point estimators, and confidence intervals for the effects to behave as theory predicts. A caveat to the above guidelines is that, when the total indirect effects are "small" in magnitude, relative to the scale of the model, convergence to the asymptotic properties appears to be very slow. Under these conditions, sampling distributions for the "smaller" valued estimates were positively skewed. This caused estimates to be significantly different from true values, and confidence intervals to behave contrary to theoretical expectations.

by Kwong-hon Ho. / Bibliography: leaves 51-53 / Thesis (M.Ph.)--Chinese University of Hong Kong, 1984