by Ying-wang Wong. / Year shown on spine: 1997. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 41-44). / Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Multiple Comparison Procedures --- p.1 / Chapter 1.2 --- Familywise Error Rate --- p.3 / Chapter 1.3 --- One-step Procedures Versus Stepwise Procedures --- p.4 / Chapter 1.4 --- Pairwise Multiple Comparisons --- p.5 / Chapter 1.5 --- Pairwise Multiple Comparisons in Two-Way Designs --- p.6 / Chapter 1.6 --- Objectives --- p.8 / Chapter 2. --- Pairwise Multiple Comparisons in One-Way Designs with Covariates --- p.9 / Chapter 2.1 --- The General ANCOVA Model --- p.9 / Chapter 2.2 --- Pairwise Comparisons --- p.12 / Chapter 3. --- Pairwise Comparisons in Two-Way Layout with Covariates --- p.15 / Chapter 3.1 --- The Model --- p.15 / Chapter 3.2 --- The Test Statistics --- p.16 / Chapter 3.3 --- Computation of Upper Percentage Points --- p.17 / Chapter 3.4 --- Approximation Procedure --- p.21 / Chapter 3.5 --- Two-Way Layout with One Covariate --- p.21 / Chapter 4. --- Numerical Examples --- p.23 / Appendix A - An Algorithm in Solving Equation (3.2.4) for the value of ta --- p.35 / Appendix B - Evaluation of Multivariate Normal Probabilities --- p.38 / References --- p.41

Project (M.S.)--Brigham Young University. Dept. of Statistics, 2004. / Includes bibliographical references (p. 109-111).

published_or_final_version / Statistics / Master / Master of Philosophy

Thesis (M. Phil.)--University of Hong Kong, 1998. / Includes bibliographical references (leaves 84-86).

It has long been presumed that any consistent nonlinear theory of a spin-two field must be generally covariant. Using Wald's consistency criteria, we exhibit classes of nonlinear theories of a spin-two field that do not have general covariance. We consider four alternative formulations of the spin-two equations. As a first example, we consider a conformally invariant theory of a spin-two field coupled to a scalar field. In the next two cases, the usual symmetric rank-two tensor field, γab, is chosen as the potential. In the fourth case, a traceless symmetric rank-two tensor field is used as the potential. We find that consistent nonlinear generalization of these different formulations leads to theories of a spin-two field that are not generally covariant. In particular, we find types of theories which, when interpreted in terms of a metric, are invariant under the infinitesimal gauge transformation γab→γab + ∇ (a∇[symbol omitted]K[symbol omitted]), where Kab is an arbitrary two-form field. In addition, we find classes of theories that are conformally invariant. As a related problem, we compare the types of theories obtained from the nonlinear extension of a divergence- and curl-free vector field when it is described in terms of two of its equivalent formulations. We find that nonlinear extension of the theory is quite different in each case. Moreover, the resulting types of nonlinear theories may not necessarily be equivalent. A similar analysis is carried out for three-dimensional electromagnetism. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

No description available.

Wong Yuen Kwan Virginia. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 85-86). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Deletion and Distance Measure --- p.6 / Chapter 2.1 --- Mahalanobis and Cook's Distances --- p.6 / Chapter 2.2 --- Defining New Measure Di --- p.8 / Chapter 2.3 --- Derivation of cov(s(i) ´ؤ s) --- p.10 / Chapter 3 --- Procedures for Detecting Influential Observations --- p.18 / Chapter 3.1 --- The One-Step Method --- p.18 / Chapter 3.1.1 --- The Method --- p.18 / Chapter 3.1.2 --- Design of Simulation Studies --- p.19 / Chapter 3.1.3 --- Results of Simulation Studies --- p.21 / Chapter 3.1.4 --- Higher Dimensional Cases --- p.24 / Chapter 3.2 --- The Forward Search Procedure --- p.24 / Chapter 3.2.1 --- Idea of the Forward Search Procedure --- p.25 / Chapter 3.2.2 --- The Algorithm --- p.26 / Chapter 4 --- Examples and Observations --- p.29 / Chapter 4.1 --- Example 1: Brain and Body Weight Data --- p.29 / Chapter 4.2 --- Example 2: Stack Loss Data --- p.34 / Chapter 4.3 --- Example 3: Percentage of Cloud Cover --- p.40 / Chapter 4.4 --- Example 4: Synthetic data of Hawkins et al.(1984) . --- p.46 / Chapter 4.5 --- Observations and Comparison --- p.52 / Chapter 5 --- Discussion and Conclusion --- p.54 / Tables --- p.56 / Figures --- p.77 / Bibliography --- p.85

The overall theme of this thesis work concerns the problem of handling measurement error and sources of variation in functional data models. The first part introduces a wavelet-based sparse principal component analysis approach for characterizing the variability of multilevel functional data that are characterized by spatial heterogeneity and local features. The total covariance of the data can be decomposed into three hierarchical levels: between subjects, between sessions and measurement error. Sparse principal component analysis in the wavelet domain allows for reducing dimension and deriving main directions of random effects that may vary for each hierarchical level. The method is illustrated by application to data from a study of human vision. The second part considers the problem of scalar-on-function regression when the functional regressors are observed with measurement error. We develop a simulation-extrapolation method for scalar-on-function regression, which first estimates the error variance, establishes the relationship between a sequence of added error variance and the corresponding estimates of coefficient functions, and then extrapolates to the zero-error. We introduce three methods to extrapolate the sequence of estimated coefficient functions. In a simulation study, we compare the performance of the simulation-extrapolation method with two pre-smoothing methods based on smoothing splines and functional principal component analysis. The third part discusses several extensions of the simulation-extrapolation method developed in the second part. Some of the extensions are illustrated by application to diffusion tensor imaging data.

Typescript (photocopy). / Digitized by Kansas Correctional Industries

The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Title from PDF of title page (University of Missouri--Columbia, viewed on March 29, 2010). Thesis advisor: Dr. Alexander Koldobsky. Vita. Includes bibliographical references.