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

Wong Kwan-to. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 50-52). / Abstracts in English and Chinese. / ACKNOWLEDGMENT --- p.iii / CHAPTER / Chapter ONE --- INTRODUCTION AND LITERATURE REVIEW --- p.1 / Chapter TWO --- THE MODEL --- p.3 / Chapter THREE --- ASYMPTOTIC BEHAVIOR OF THE LEAST SQUARES ESTIMATORS --- p.6 / Chapter FOUR --- EIGHT SPECIAL CASES --- p.12 / Chapter FIVE --- MONTE CARLO EXPERIMENTS --- p.36 / Chapter SIX --- CONCLUSION --- p.40 / APPENDIX --- p.41 / BIBLIOGRAPHY --- p.50

by Chun-Wai Sit. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 91-92). / Abstract also in Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Ridge Regression --- p.3 / Chapter 1.2 --- Generalized Ridge Regression and Present Work --- p.11 / Chapter Chapter 2 --- Shrinkage Estimation of Regression Coefficients --- p.14 / Chapter 2.1 --- Introduction --- p.15 / Chapter 2.2 --- Dominance over the Least Squares Estimator --- p.17 / Chapter 2.3 --- Dominance over the Ridge Estimator --- p.26 / Chapter 2.4 --- Bayesian Motivation --- p.31 / Chapter 2.5 --- Choosing the Shrinkage Factor --- p.33 / Chapter 2.5.1 --- Generalized Cross-Validation (GCV) --- p.34 / Chapter 2.5.2 --- RIDGM --- p.35 / Chapter 2.5.3 --- Iterative method for selecting the optimum parameter (IA) --- p.38 / Chapter 2.5.4 --- Empirical Bayes Approach --- p.45 / Chapter Chapter 3 --- Simulation Study --- p.47 / Chapter 3.1 --- Simulation Plan --- p.48 / Chapter 3.2 --- Simulation Result --- p.54 / Chapter 3.2.1 --- β = βL --- p.55 / Chapter 3.2.2 --- β = βs --- p.61 / Chapter 3.3 --- Average k and a --- p.67 / Chapter 3.3.1 --- Shrinkage Estimator --- p.67 / Chapter 3.3.2 --- Ridge Estimator --- p.78 / Chapter 3.4 --- Conclusion --- p.88 / References --- p.91

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In this thesis we introduce and study the (i) Grassmannian, (ii) Lagrangian Grassmannian, and (iii) double Lagrangian Grassmannian of subspaces in ( A ⊗ B )n, where A and B are normed division algebras, i.e. R,C,H or O . / This gives a simple and uniform description of all symmetric spaces. This is analogous to Tits magic square description for simple Lie algebras. / We show that every irreducible compact Riemannian symmetric space X must be one of these Grassmannian spaces (up to a finite cover) or a compact simple Lie group. Furthermore, its noncompact dual symmetric space is the open sub-manifold of X consisting of spacelike linear subspaces, at least in the classical cases. / Huang, Yongdong. / "July 2007." / Adviser: Naichung Conan Leung. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0353. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 64-65). / 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. / Abstracts in English and Chinese. / School code: 1307.

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A methodology for the construction of predictive empirical models of physiological characteristics from microarray data is presented. The method, applied here to the study of the development of diabetes and insulin resistance, can be further expanded to other cases and to also include a variety of other data, such as protein expression, or metabolic flux data. The importance of several of the genes identified by the modeling methodology can be verified by comparison with results from prior literature. This implies potentially significant roles in diabetes for several of the uncharacterized genes discovered during the modeling procedure. / Singapore-MIT Alliance (SMA)

In this thesis, we develop and test a fundamentally new linear-discontinuous least-squares (LDLS) method for spatial discretization of the one-dimensional (1-D) discrete-ordinates (SN) equations. This new scheme is based upon a least-squares method with a discontinuous trial space. We implement our new method, as well as the lineardiscontinuous Galerkin (LDG) method and the lumped linear-discontinuous Galerkin (LLDG) method. The implementation is in FORTRAN. We run a series of numerical tests to study the robustness, L2 accuracy, and the thick diffusion limit performance of the new LDLS method. By robustness we mean the resistance to negativities and rapid damping of oscillations. Computational results indicate that the LDLS method yields a uniform second-order error. It is more robust than the LDG method and more accurate than the LLDG method. However, it fails to preserve the thick diffusion limit. Consequently, it is viable for neutronics but not for radiative transfer since radiative transfer problems can be highly diffusive.

In this thesis, we study the least trimmed squares artificial neural networks (LTS-ANNs), which are generalization of the least trimmed squares (LTS) estimators frequently used in robust linear parametric regression problems to nonparametric artificial neural networks (ANNs) used for nonlinear regression problems. Two training algorithms are proposed in this thesis. The first algorithm is the incremental gradient descent algorithm. In order to speed up the convergence, the second training algorithm is proposed based on recursive least squares (RLS). Three illustrative examples are provided to test the performances of robustness against outliers for the classical ANNs and the LTS-ANNs. Simulation results show that upon proper selection of the trimming constant of the learning machines, LTS-ANNs are quite robust against outliers compared with the classical ANNs.

In recent years, the main determinants of gold price have changed worldwide due to the increasing demand of gold. Additionally, TAIFEX provided investors with anothor trading instruments by launching US Dollar-denominated Gold Futures. Therefore, Taiwan gold market and stock market might interact more closely than before. The purpose of this study was to examine the endogenous relationship between gold price and stock price, and then analyze both markets with multi-equation simulation model and two-stage least squares method. The result shows that there is endogenous relationship between these two variables. Besides, depreciation of US dollar would lead to a rise in gold price which is denominated by US dollar. Exchange rate and stock price also moved in opposite directions. Finally, the launching of gold futures truly interested the investors and boosted the gold price.