Cheung Shu Fai. / "August 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 117-123). / 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.

This thesis includes three parts. The overarching theme is how to analyze multilevel structured datasets, particularly in the areas of survey and causal inference. The first part discusses model selection of hierarchical models, in the context of a national political survey. I found that the commonly used model selection criteria based on predictive accuracy, such as cross validation, don't perform very well in the case of political survey and explore the possible causes. The second part centers around a unique data set on the presidential election collected through an online platform. I show that with adequate modeling, meaningful and highly accurate information could be extracted from this highly-biased data set. The third part builds on a formal causal inference framework for group-structured data, such as meta-analysis and multi-site trials. In particular, I develop a Gaussian Process model under this framework and demonstrate additional insights that can be gained compared with traditional parametric models.

We consider several problems motivated by issues faced in the mining industry. In recent years, it has become clear that mines have substantial tail risk in the form of environmental disasters, and this tail risk is not incorporated into common pricing and risk models. However, data sets of the extremal climate behavior that drive this risk are very small, and generally inadequate for properly estimating the tail behavior. We propose a data-driven methodology that comes up with reasonable worst-case scenarios, given the data size constraints, and we incorporate this into a real options based model for the valuation of mines. We propose several different iterations of the model, to allow the end-user to choose the degree to which they wish to specify the financial consequences of the disaster scenario. Next, in order to perform a risk analysis on a portfolio of mines, we propose a method of estimating the correlation structure of high-dimensional max-stable processes. Using the techniques of (Liu Et al, 2017) to map the relationship between normal correlations and max-stable correlations, we can then use techniques inspired by (Bickel et al, 2008, Liu et al, 2014, Rothman et al, 2009) to estimate the underlying correlation matrix, while preserving a sparse, positive-definite structure. The correlation matrices are then used in the calculation of model-robust risk metrics (VaR, CVAR) using the the Sample-Out-of-Sample methodology (Blanchet and Kang, 2017). We conclude with several new techniques that were developed in the field of robust performance analysis, that while not directly applied to mining, were motivated by our studies into distributionally robust optimization in order to address these problems.

Sin Ka Yu = 抽取臉孔特徵及辨認臉孔的統計學方法 / 冼家裕. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 86-90). / Text in English; abstracts in English and Chinese. / Sin Ka Yu = Chou qu lian kong te zheng ji bian ren lian kong de tong ji xue fang fa / Xian Jiayu. / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1. --- Motivation --- p.1 / Chapter 1.2. --- Objectives --- p.4 / Chapter 1.3. --- Organization of the thesis --- p.4 / Chapter Chapter 2. --- Facial Feature Extraction --- p.6 / Chapter 2.1. --- Introduction --- p.6 / Chapter 2.2. --- Reviews of Statistical Approach --- p.8 / Chapter 2.2.1. --- Eigenfaces --- p.8 / Chapter 2.2.1.1. --- Eigenfeatures Error! Bookmark not defined / Chapter 2.2.3. --- Singular Value Decomposition --- p.14 / Chapter 2.2.4. --- Summary --- p.15 / Chapter 2.3. --- Review of fiducial point localization methods --- p.16 / Chapter 2.3.1. --- Symmetry based Approach --- p.16 / Chapter 2.3.2. --- Color Based Approaches --- p.17 / Chapter 2.3.3. --- Integral Projection --- p.17 / Chapter 2.3.4. --- Deformable Template --- p.20 / Chapter 2.4. --- Corner-based Fiducial Point Localization --- p.22 / Chapter 2.4.1. --- Facial Region Extraction --- p.22 / Chapter 2.4.2. --- Corner Detection --- p.25 / Chapter 2.4.3. --- Corner Selection --- p.27 / Chapter 2.4.3.1. --- Mouth Corner Pairs Detection --- p.27 / Chapter 2.4.3.2. --- Iris Detection --- p.27 / Chapter 2.5. --- Experimental Results --- p.30 / Chapter 2.6. --- Conclusions --- p.30 / Chapter 2.7. --- Notes on Publications --- p.30 / Chapter Chapter 3. --- Fiducial Point Extraction with Shape Constraint --- p.32 / Chapter 3.1. --- Introduction --- p.32 / Chapter 3.2. --- Statistical Theory of Shape --- p.33 / Chapter 3.2.1. --- Shape Space --- p.33 / Chapter 3.2.2. --- Shape Distribution --- p.34 / Chapter 3.3. --- Shape Guided Fiducial Point Localization --- p.38 / Chapter 3.3.1. --- Shape Constraints --- p.38 / Chapter 3.3.2. --- Intelligent Search --- p.40 / Chapter 3.4. --- Experimental Results --- p.40 / Chapter 3.5. --- Conclusions --- p.42 / Chapter 3.6. --- Notes on Publications --- p.42 / Chapter Chapter 4. --- Statistical Pattern Recognition --- p.43 / Chapter 4.1. --- Introduction --- p.43 / Chapter 4.2. --- Bayes Decision Rule --- p.44 / Chapter 4.3. --- Gaussian Maximum Probability Classifier --- p.46 / Chapter 4.4. --- Maximum Likelihood Estimation of Mean and Covariance Matrix --- p.48 / Chapter 4.5. --- Small Sample Size Problem --- p.50 / Chapter 4.5.1. --- Dispersed Eigenvalues --- p.50 / Chapter 4.5.2. --- Distorted Classification Rule --- p.55 / Chapter 4.6. --- Review of Methods Handling the Small Sample Size Problem --- p.57 / Chapter 4.6.1. --- Linear Discriminant Classifier --- p.57 / Chapter 4.6.2. --- Regularized Discriminant Analysis --- p.59 / Chapter 4.6.3. --- Leave-one-out Likelihood Method --- p.63 / Chapter 4.6.4. --- Bayesian Leave-one-out Likelihood method --- p.65 / Chapter 4.7. --- Proposed Method --- p.68 / Chapter 4.7.1. --- A New Covariance Estimator --- p.70 / Chapter 4.7.2. --- Model Selection --- p.75 / Chapter 4.7.3. --- The Mixture Parameter --- p.76 / Chapter 4.8. --- Experimental results --- p.77 / Chapter 4.8.1. --- Implementation --- p.77 / Chapter 4.8.2. --- Results --- p.79 / Chapter 4.9. --- Conclusion --- p.81 / Chapter 4.10. --- Notes on Publications --- p.82 / Chapter Chapter 5. --- Conclusions and Future works --- p.83 / Chapter 5.1. --- Conclusions and Contributions --- p.83 / Chapter 5.2. --- Future Works --- p.84

現代風險管理需要對金融產品的相關結構做出刻畫，而在實際生活中，我們通常使用相關係數和自相關係數去刻畫這種結構。然而，越來越多的人意識到自相關函數在度量相關結構上面被高估了，特別是在風險管理中我們更關心極端事件。同樣的，偏自相關函數也有這樣的短板。在這篇論文中，我們在有限維分佈服從有正尾係數的正則變差的嚴平穩過程上定義了Partial Extremogram。 這個指標僅僅依賴於隨機過程中的極端值。我們給出了它的一個估計并且研究了這個估計的漸進性質。此外，为了刻畫时间序列的負相關結構，我們把 Inverse Tail Dependence 的想法推廣到了隨機過程上面並且引入了Inverse Extremogram 的概念。我們給出了Inverse Extremogram 在ARMA模型中的顯示表達式。理論推導和數據模擬都說明這個指標可以很好的刻畫出一個隨機過程的尾部的負相關結構。 / Modern risk management calls for deeper understanding of the dependence structure of financial products, which is usually measured by correlation or autocorrelation functions. More and more people realized that autocorrelation function is overvalued as a tool to measure dependence, especially when one has to deal with extremal events in risk management. Likewise, partial autocorrelation function also suffers similar shortcomings as autocorrelation function. In this thesis, an analog of the partial autocorrelation function for a strictly stationary sequence of random variables whose finite-dimensional distributions are jointly regularly varying with positive index, the partial extremogram, is introduced. This function only depends on the extremal events of the underlying process. A natural estimator of the partial extremogram is also proposed and its asymptotic properties are studied. Furthermore, to measure the negative dependence of a time series, the idea of inverse tail dependence is extended to a stochastic process and the notion of inverse extremogram is proposed. A closed form of the inverse extremogram for an ARMA model is deduced. The theoretical and simulation results show that the inverse extremogram is a useful tool for measuring the negative tail dependence of a process. / Detailed summary in vernacular field only. / Chen, Pengcheng. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 53-56). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Tail Dependence --- p.2 / Chapter 1.2 --- Extremogram --- p.4 / Chapter 1.2.1 --- Regularly Varying Time Series --- p.4 / Chapter 1.2.2 --- Extremogram for Regularly Varying Time Series --- p.7 / Chapter 1.3 --- Motivation and Organization --- p.8 / Chapter 2 --- Partial Extremogram --- p.9 / Chapter 2.1 --- Definition of Partial Extremogram --- p.9 / Chapter 2.2 --- Applications of Partial Extremogram --- p.15 / Chapter 2.2.1 --- AR(1) Process --- p.15 / Chapter 2.2.2 --- MA(1) process --- p.17 / Chapter 2.2.3 --- Stochastic Volatility Model --- p.19 / Chapter 2.3 --- Estimation of Partial Extremogram --- p.19 / Chapter 2.4 --- Simulation Study --- p.22 / Chapter 3 --- Inverse Extremogram --- p.28 / Chapter 3.1 --- Definition of Inverse Extremogram --- p.28 / Chapter 3.2 --- Applications of Inverse Extremogram --- p.29 / Chapter 3.2.1 --- MA(q) Model --- p.29 / Chapter 3.2.2 --- MA(∞) Model --- p.35 / Chapter 3.2.3 --- ARMA Model --- p.40 / Chapter 3.2.4 --- GARCH Model and SV Model --- p.41 / Chapter 3.3 --- Simulation Study --- p.42 / Chapter 4 --- Conclusions and Further Research --- p.50 / Bibliography --- p.53

Cheung Wai-leung. / "July 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 110-129). / 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.

Wong Hing-Kwok. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 34-35). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Radial Basis Function (RBF) of Neural Network --- p.5 / Chapter 2.1 --- Neural Network --- p.6 / Chapter 2.2 --- Radial Basis Function (RBF) Network --- p.8 / Chapter 2.3 --- Model Specification --- p.10 / Chapter 2.4 --- Estimation --- p.12 / Chapter 3 --- RBF in Performance Attribution --- p.17 / Chapter 3.1 --- Background of Data Set --- p.18 / Chapter 3.2 --- Portfolio Construction --- p.20 / Chapter 3.3 --- Portfolio Rebalance --- p.22 / Chapter 3.4 --- Result --- p.23 / Chapter 4 --- Comparison --- p.26 / Chapter 4.1 --- Standard Linear Model --- p.27 / Chapter 4.2 --- Fixed Additive Model --- p.28 / Chapter 4.3 --- Refined Additive Model --- p.29 / Chapter 4.4 --- Result --- p.30 / Chapter 5 --- Conclusion --- p.32 / Bibliography --- p.34

Shum Chun-Yin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 63-64). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Ordinal Contingency Table --- p.5 / Chapter 2.1 --- Model --- p.5 / Chapter 2.2 --- The Maximum Likelihood Method --- p.7 / Chapter 2.3 --- Limitation of the Maximum Likelihood Estimation in Large Sample --- p.8 / Chapter 2.4 --- The Partition Maximum Likelihood Approach --- p.9 / Chapter 3 --- Modification of the Partition Maximum Likelihood Approach --- p.12 / Chapter 3.1 --- The Modified Partition Maximum Likelihood Approach --- p.12 / Chapter 3.2 --- Mx Implementation --- p.14 / Chapter 3.2.1 --- Maximum Likelihood Procedure --- p.14 / Chapter 3.2.2 --- Modified PML Procedure --- p.15 / Chapter 3.3 --- Examples --- p.16 / Chapter 3.3.1 --- Example 1 : Attitudes of Morality and Equality --- p.16 / Chapter 3.3.2 --- Example 2 : A Panel Model for Political Efficacy --- p.17 / Chapter 3.4 --- Limitation of the Modified PML Approach --- p.19 / Chapter 3.5 --- Simulation Study for the Modified PML Approach --- p.20 / Chapter 4 --- Generalization to Structural Equation Model --- p.22 / Chapter 4.1 --- Model --- p.23 / Chapter 4.2 --- Procedure --- p.24 / Chapter 4.3 --- Examples --- p.26 / Chapter 4.3.1 --- Example 1 : Attitudes of Morality and Equality --- p.26 / Chapter 4.3.2 --- Example 2 : A Panel Model for Political Efficacy --- p.28 / Chapter 5 --- Generalization to Stochastic Constraints on Thresholds --- p.31 / Chapter 5.1 --- Model --- p.32 / Chapter 5.2 --- Bayesian Analysis of the Model --- p.33 / Chapter 5.3 --- Examples --- p.35 / Chapter 5.3.1 --- Example 1 : Attitudes of Morality and Equality --- p.35 / Chapter 5.3.2 --- Example 2 : A Panel Model for Political Efficacy --- p.36 / Chapter 6 --- Conclusion and Discussion --- p.38 / Chapter A --- Mx Script of the ML Estimation - for Example 1 --- p.40 / Chapter B --- Mx Script of the Modified PML Estimation - for Example 1 --- p.42 / Chapter C --- Mx Script of the Modified PML Estimation - for Example 2 --- p.45 / Bibliography --- p.63

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