by Chun-nam Lau. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1988. / Bibliography: leaves 85-89.

by Wing-yi, Tam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 74-77). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Cox and Lewis' Model and Weibull Process Model / Chapter Section 1 --- Nonhomogeneous Poisson Process (NHPP) --- p.5 / Chapter Section 2 --- Cox and Lewis' Model --- p.7 / Chapter Section 3 --- Weibull Process Model --- p.11 / Chapter Section 4 --- Test of NHPP --- p.14 / Chapter Chapter 3 --- Inference for Geometric Process with Inverse Gaussian Distribution / Chapter Section 1 --- Geometric Process (GP) --- p.18 / Chapter Section 2 --- Inverse Gaussian Distribution (IG) --- p.22 / Chapter Section 3 --- Simulation --- p.25 / Chapter Section 4 --- Conclusion --- p.33 / Chapter Chapter 4 --- Comparison Geometric Process Model and NHPP model in Fitting a Point Process / Chapter Section 1 --- Introduction --- p.34 / Chapter Section 2 --- Real Data Examples --- p.39 / Chapter Section 3 --- Conclusion --- p.45 / Tables and Graphs --- p.48 / Appendices --- p.71 / References --- p.74

在許多實驗研究中，實驗數據經常由有序觀測數據組成，這樣的例子很容易在醫學、臨床研究、社會學或心理學的研究中找到。一般有兩種方法可以用來分析有序分類數據。第一種方法是基於Wilcoxon-Mann-Whitney 統計量的非參數方法，第二種方法是把響應變量看成是某個連續潛變量模型的一種表現的潛變量模型。在本論文中，我們主要研究基於潛變量模型對具有一維或二維有序分類響應變量的處理的比較問題，同時解決具有一維有序分類數據的多重比較過程的功效及樣本量的確定問題。 / 潛變量模型已經被應用于對具有一維有序分類觀測數據的含有對照組的多重比較中。這種方法可以很好地應用于臨床研究中對含有對照組的不同治療方法的效用比較問題。在本論文的第一部份中，我們致力於把這種思想推廣到成對多重比較，成對多重比較是臨床研究中另一個很重要的課題。我們通過隨機模擬來對不同的方法在控制整體第一類錯誤和功效的優勢進行評估。在本論文的第二部份，我們主要研究具有二維有序分類響應變量的多重比較過程。在這些過程中，我們把二維有序分類數據看成是某個潛二維變量的一種表現。非參數方法也經常被應用於做兩個處理的比較問題。然而在本文中，我們對非參數方法的劣勢進行了說明。處理具有二維有序分類響應變量的含有對照組的多重比較問題是本論文的研究重點。基於潛變量模型的方法，我們給出了含有對照組的多重比較的若干檢驗過程，包括單步檢驗過程和逐步檢驗過程。在論文的第三部份，我們對具有一維有序分類數據的含有對照組的多重比較過程的功效和樣本量的確定問題進行了討論。基於Lu, Poon and Cheung (2012) 建議的多重比較過程，我們得到了滿足一定功效的樣本量的確定方法，并通過實例進行了說明。 / In many scientific studies, research data are frequently composed of ordered categorical observations. Numerous examples could easily be found in areas including medical and clinical studies, sociology and psychology. There are two popular approaches in analyzing ordered categorical data. One is to employ the non-parametric method based on the Wilcoxon-Mann-Whitney statistics. The other is to use the latent variable model that conceptualizes the responses as manifestations of some underlying continuous variables. In this project, we focus on the comparisons of different populations with either univariate or bivariate ordered categorical observations using a latent variable model. The study of power and sample size requirement for multiple testing with univariate ordered categorical data are also provided in this thesis. / For univariate ordered categorical observations, the latent variable model has been used to compare treatments with a control. The developed methods are useful for applications in clinical studies where one would like to compare the efficacy of different treatments with a given control/placebo. In this thesis, we seek to extend this idea to develop the useful procedures for pairwise multiple comparisons which are often important objectives of clinical trials. Extensive simulation studies regarding overall type I error rate and power are performed to evaluate the merits of different procedures. / The second part of this thesis is devoted to multiple comparison methods with bivariate ordered categorical responses under the assumption that the bivariate ordered categorical data are manifestations of an underlying bivariate normal distribution. To compare two population mean vectors, nonparametric procedures are also frequently being used, but as demonstrated in this thesis, these methods are inferior to testing procedures based on the latent variable model. Hence, by the adoption of the latent variable model, we develop procedures that can be used to conduct multiple comparisons with a control for bivariate categorical responses. Different multiple comparison mechanisms including single-step and stepwise procedures are explored. Numerical examples for illustrative purposes are also given. / For the last part of this thesis, we discuss power and sample size determination for multiple comparisons with control for univariate ordered categorical data. Based on the multiple testing procedures proposed by Lu, Poon and Cheung (2012), we derive the procedure to compute the required sample size that guarantee a pre-specified power level. Numerical examples are also given. / For the last part of this thesis, we discuss power and sample size determination for multiple comparisons with control for univariate ordered categorical data. Based on the multiple testing procedures proposed by Lu, Poon and Cheung (2012), we derive the procedure to compute the required sample size that guarantee a pre-specified power level. Numerical examples are also given. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Lin, Yueqiong. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 92-100). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Overview --- p.1 / Chapter 1.2 --- Outline of the thesis --- p.4 / Chapter 2 --- Pairwise Comparisons with Ordered Categorical Responses --- p.6 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Proportional odds model --- p.8 / Chapter 2.3 --- Latent variable model --- p.11 / Chapter 2.4 --- Pairwise comparisons --- p.15 / Chapter 2.4.1 --- Single-step procedure and the computation of critical values . --- p.15 / Chapter 2.4.2 --- Approximation of critical values --- p.16 / Chapter 2.4.3 --- A single-step conservative testing procedure: the Bonferroni procedure --- p.18 / Chapter 2.4.4 --- A step-wise testing procedure: Hochberg's step-up procedure . --- p.19 / Chapter 2.5 --- Simulation: power comparison --- p.20 / Chapter 2.6 --- Examples --- p.24 / Chapter 2.7 --- Conclusion --- p.28 / Chapter 3 --- Multiple comparison procedures for a latent variable model with bivariate ordered categorical responses --- p.29 / Chapter 3.1 --- Introduction --- p.29 / Chapter 3.2 --- Latent bivariate normal model --- p.31 / Chapter 3.2.1 --- The model --- p.31 / Chapter 3.2.2 --- Model specification --- p.33 / Chapter 3.2.3 --- Test Statistics --- p.35 / Chapter 3.2.4 --- Statistical inference --- p.35 / Chapter 3.3 --- Nonparametric test --- p.37 / Chapter 3.3.1 --- Test statistic --- p.39 / Chapter 3.3.2 --- A Comparison between the latent variable model procedure and nonparametric tests --- p.42 / Chapter 3.4 --- Multiple comparisons of several treatments with a control based on the latent variable model --- p.47 / Chapter 3.5 --- Simulation --- p.51 / Chapter 3.6 --- Examples --- p.56 / Chapter 3.7 --- Conclusion --- p.59 / Chapter 4 --- Sample size determination for multiple comparisons with ordered univariate categorical data --- p.62 / Chapter 4.1 --- Introduction --- p.62 / Chapter 4.2 --- Multiple comparisons of treatments a control with ordered categorical responses --- p.64 / Chapter 4.3 --- Power function --- p.67 / Chapter 4.4 --- Sample size determination and tables --- p.75 / Chapter 4.5 --- Examples --- p.85 / Chapter 4.6 --- Conclusion --- p.88 / Chapter 5 --- Further Research --- p.90 / Bibliography --- p.92 / Appendix / Chapter A --- Procedures to obtain the MLE of parameter θ₀ --- p.101 / Chapter B --- Nonparametric test --- p.105 / Chapter C --- Procedures to obtain the critical value for Dunnett's single-step procedure --- p.109 / Chapter D --- Procedures to obtain the critical value for Dunnett's single-step procedure with balanced homogeneous groups --- p.112

This thesis deals with estimation and inference in two semiparametric problems: a two-component mixture model and a single index regression model. For the two-component mixture model, we assume that the distribution of one component is known and develop methods for estimating the mixing proportion and the unknown distribution using ideas from shape restricted function estimation. We establish the consistency of our estimators. We find the rate of convergence and the asymptotic limit of our estimator for the mixing proportion. Furthermore, we develop a completely automated distribution-free honest finite sample lower confidence bound for the mixing proportion. We compare the proposed estimators, which are easily implementable, with some of the existing procedures through simulation studies and analyse two data sets, one arising from an application in astronomy and the other from a microarray experiment. For the single index model, we consider estimation of the unknown link function and the finite dimensional index parameter. We study the problem when the true link function is assumed to be: (1) smooth or (2) convex. When the link function is just assumed to be smooth, in contrast to standard kernel based methods, we use smoothing splines to estimate the link function. We prove the consistency and find the rates of convergence of the proposed estimators. We establish root-n-rate of convergence and the semiparametric efficiency of the parametric component under mild assumptions. When the link function is assumed to be convex, we propose a shape constrained penalized least squares estimator and a Lipschitz constrained least squares estimator for the unknown quantities. We prove the consistency and find the rates of convergence for both estimators. For the shape constrained penalized least squares estimator, we establish root-n-rate of convergence and the semiparametric efficiency of the parametric component under mild assumptions and conjecture that the parametric component of the Lipschitz constrained least squares estimator is semiparametrically efficient. We develop the R package "simest'' that can be used (to compute the proposed estimators) even for moderately large dimensions.

In this thesis, we first propose a coherent inference model that is obtained by distorting the prior density in Bayes' rule and replacing the likelihood with a so-called pseudo-likelihood. This model includes the existing non-Bayesian inference models as special cases and implies new models of base-rate neglect and conservatism. We prove a sufficient and necessary condition under which the coherent inference model is processing consistent, i.e., implies the same posterior density however the samples are grouped and processed retrospectively. We show that processing consistency does not imply Bayes' rule by proving a sufficient and necessary condition under which the coherent inference model can be obtained by applying Bayes' rule to a false stochastic model. We then propose a prediction model that combines a stochastic model with certain parameters and a processing-consistent, coherent inference model. We show that this prediction model is processing consistent, which states that the prediction of samples does not depend on how they are grouped and processed prospectively, if and only if this model is Bayesian. Finally, we apply the new model of conservatism to a car selection problem, a consumption-based asset pricing model, and a regime-switching asset pricing model.

The term relationship in a general statistical concept connotes a wide range of meanings and applications. However, the resultant meaning of the term usually focus on the principle of connectivity, association, causation, inter-relationship, or linkages between variables. In view of this, the thesis reports on the statistical relationships between GDP, Inflation, Export and import. The study utilized 65 countries with data ranging from 1970 to 2011. The research, which is an applied empirical, involves two phases. The first phase dealt with the exploration of nature and pattern of Granger causality concept by using GDP and inflation. In this phase, we first ensured the stationarity and stability of our time series variables are maintained. The stationary and non-stationary instruments utilized include ADF, PP, KPSS, Chow and Quandt tests. After these, we carried out extensive computations using the Granger causality. It should be noted that the concept of Granger causality is concerned with how a variable X can enhance or better the prediction of other variable Y by using the principle of cause and effect. In the second phase of the study, we explored the possible linkages of exports and imports to the Granger causality of GDP and Inflation that were established in Phase 1. To achieve this, we first carried out pairwise Granger causality tests on the four variables (GDP, Inflation, Export and Import) and then considered further computations and testing on the said variables by utilizing the principles of Bayes theorem, assignment problem models, coefficient of variation and other relevant statistical concepts. In fact, the results at this phase are the major contributions to knowledge. The general description of the study embraced the conceptual steps, where we considered relevant literatures on Granger causality and theory of some statistical principles and practices as earlier mentioned above. Next, we have the empirical studies description in which the methodology, results/findings and interpretations on the study were considered. Based on our findings, we conclude that Inflation “Granger causes” GDP most often occurred than the other combinations of Granger causality between Inflation and GDP. Also, it was established that countries with developed economies supported the Granger causality concept better than the developing economies. This result can be attributed to the stability of most of the developed economy variables, while it is unstable with most of the developing economy countries. With countries supporting Granger causality, we have uniformly distributed pattern for the three types in the developed economies whilst skewed toward Inflation “Granger causes” GDP for the developing economies. For other important conclusions, we could establish that less volatility of export over import supports the bidirectional Granger causality whilst higher volatility of exports over import is relationally linked to the unidirectional Granger causality. We inferred also that when there is unidirectional Granger causality between inflation and import (or export), there is also unidirectional causality between GDP and inflation by the Bayes' Rule; and when there is bidirectional Granger causality between GDP and import only, there is bidirectional causality between GDP and inflation.

Tam Ha-ting. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 93-106). / Abstracts in English and Chinese. / Declaration --- p.2 / Acknowledgement --- p.3 / Abstract --- p.4 / 本文摘要 --- p.5 / Chapter Chapter 1 --- Introduction --- p.8 / Chapter §1.1 --- The role of examination in the Hong Kong education system / Chapter §1.2 --- Examination-oriented approach and teaching / Chapter §1.3 --- Examination-oriented approach and learning / Chapter §1.4 --- Cross-cultural comparisons / Chapter §1.5 --- Evolution and impact of learning theories / Chapter §1.6 --- The layout of this thesis / Chapter Chapter 2 --- Behavioral and cognitive approaches to learning --- p.15 / Chapter §2.1 --- Introduction / Chapter §2.2 --- Behavioral approach / Chapter §2.3 --- Ivan. Pavlov: Classical conditioning / Chapter §2.4 --- B. F. Skinner: Operant conditioning / Chapter §2.5 --- Components of behavioral learning / Chapter 2.5.1 --- The role of consequences / Chapter 2.5.2 --- Schedule of reinforcements / Chapter 2.5.3 --- Shaping / Chapter 2.5.4 --- Stimulus control / Chapter §2.6 --- The impact of behavioral approach to teaching and learning / Chapter §2.7 --- Evaluation of behavior approach / Chapter §2.8 --- Rise of cognitive psychology / Chapter Chapter 3 --- Constructivism --- p.35 / Chapter §3.1 --- Nature of knowledge / Chapter §3.2 --- The acquisition of knowledge / Chapter §3.3 --- Constructivist view of learning / Chapter §3.4 --- Piaget and constructivism / Chapter §3.5 --- The impact of constructivism on teaching and learning / Chapter §3.6 --- Evaluation of constructivism / Chapter Chapter 4 --- Constructivist approach to statistics learning --- p.62 / Chapter §4.1 --- Constructivist approach to science learning / Chapter 4.1.1 --- Physics instruction / Chapter 4.1.2 --- Mathematics instruction / Chapter §4.2 --- Constructivism and ill-structured discipline / Chapter 4.2.1 --- Nature of ill-structured domain: Conceptual complexity and across-case irregularity / Chapter 4.2.2 --- Statistics as an ill-structured discipline / Chapter 4.2.3 --- "Example: Statistics in sociology, 1950 -2000" / Chapter 4.2.4 --- Constructivism based teaching strategies in ill-structured domain / Chapter §4.3 --- Development of on-line teaching / Chapter 4.3.1 --- Multiple representation of information / Chapter 4.3.2 --- Interactive between users and the information / Chapter Chapter 5 --- Case study --- p.83 / Chapter §5.1 --- Description of workshop / Chapter §5.2 --- Features of workshop / Chapter §5.3 --- Evaluation / Chapter Chapter 6 --- Conclusions --- p.91 / Bibliography --- p.93

In general model selection so far considered in literature, the parameter estimation loss and the prediction loss from the model selected are considered to be the same. In this thesis, the methods of parameter estimation may vary with different estimation loss, and the model selection may be based on different prediction loss. Under some regularized conditions, a model selection criterion, called generalized risk criterion (GRC), is proposed with a closed form. For multivariate linear regression model, and Cox regression model for ranking data, our studies that this criterion is an extension of the model selection criterion AIC. We also demonstrate that GRC performs better than AIC in a practical semi-parametric regression problem involving investments on horse racing. / Keywords: Variable selection; Model selection criterion; AIC; GRC; Loss function; Risk function; Multinomial Choice Model; Cox model for ranking data. / Searching for the true model based on the limited data is usually an impossible task. More and more attention in research has been focused on how to find an optimal model based on some special objective, such as focused information criterion (FIC, Hjort and Claeskens, 2003 [15]), Subspace Information criterion (Sugiyama and Ogawa, 2001 [43]) in statistical learning, etc. These ideas also motivate us to find an optimal subset of variables based on some objective. Different objectives may result in different choices of subset of variables. / Variable selection, an important aspect of model selection, is applied widely in real practices to explore the latent relationship between the random phenomena and various factors. Many model selection criteria, such as Mallow's Cp (Mallows, 1964 [28]). PRESS (Allen, 1971 [3]). AIC (Akaike, 1973 [2]), are proposed for seeking the optimal subset of the variables. Most of them try to find a criterion based on the observed data such that the selected models perform well both for fitting and for prediction. / Zuo, Guo Xin. / "July 2007." / Adviser: Ming Gao Gu. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0402. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 71-75) / 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.

Lin Jianzhong. / "May 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 106-118). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

The Standard Model of cosmology successfully describes the observable Universe requiring only a small number of free parameters. The model has been validated by a wide range of observable probes such as Supernovae IA, the CMB, Baryonic Acoustic Oscillations and galaxy clusters. Weak Gravitational Lensing (WL) is becoming a popular observational technique to constrain parameters in the Standard Model and is particularly appealing to the scientific community because the tracers it relies on, image distortions, are unbiased probes of density fluctuations in the fabric of the cosmos. The WL effect is sensitive to the late time evolution of the Universe, in which structures are non--linear. Because of this, WL observations cannot be treated as Gaussian random fields and statistical information on cosmology leaks from quadratic correlations into more complicated, higher order, image features. The goal of this dissertation is to analyze the efficiency of some of these higher order features in constraining Standard Model parameters. We approach the investigation from a practical point of view, examining the analytical, computational and numerical accuracy issues that are involved in carrying a complete analysis from observational data to parameter constraints using these higher order statistics. This work is organized as follows: - In Chapter 1 we review the fundamentals of the LambdaCDM Standard Model of cosmology, focusing particularly on the Friedmann picture and on the physics of large scale density fluctuations. - In Chapter 2 we give an outline of the Gravitational Lensing effect in the context of cosmology, and we introduce the basic WL observables from an analytical point of view. - In Chapter 3 we review the relevant numerical techniques used in the modeling of WL observables, focusing in particular on the algorithms used in ray--tracing simulations. These simulations constitute the base of our modeling efforts. - In Chapter 4 we discuss feature extraction techniques from WL observations: we treat both quadratic statistics, such as the angular shear--shear power spectrum, and higher order statistics for which analytical treatment is not possible. - In Chapter 5 we review the Bayesian formalism behind the inference of LambdaCDM parameters from image features. We place particular emphasis on physical and numerical effects that degrade parameter constraints and discuss possible mitigations. -In Chapter 6 we apply the previously described techniques to the Canada France Hawaii LenS galaxy survey, showing how the use of higher order image statistics can improve inferences on the LambdaCDM parameters that describe density fluctuations. - In Chapter 7 we discuss some of the issues that arise in the analysis of a large scale WL survey such as the Large Scale Synoptic Survey: we focus on systematic effects caused by sensors imperfections, the atmosphere, redshift errors and approximate theoretical modeling. - In Chapter 8 we draw our conclusions and discuss possible future developments.