Li Guo-Yin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 105-107). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Examples for the variational inequality problem --- p.2 / Chapter 1.2 --- Approaches for variational inequality problem --- p.7 / Chapter 1.3 --- Error bounds results for variational inequality problem --- p.8 / Chapter 1.4 --- Organization --- p.9 / Chapter 2 --- Solution Theory --- p.11 / Chapter 2.1 --- "Elementary Convex Analysis, Nonsmooth Analysis and Degree theory" --- p.11 / Chapter 2.1.1 --- Elementary Convex Analysis --- p.11 / Chapter 2.1.2 --- Elementary Nonsmooth Analysis --- p.16 / Chapter 2.1.3 --- Degree Theory --- p.18 / Chapter 2.2 --- Existence and Uniqueness Theory --- p.24 / Chapter 3 --- Merit Functions for variational inequalities problem --- p.36 / Chapter 3.1 --- Regularized gap function --- p.38 / Chapter 3.2 --- D-gap function --- p.44 / Chapter 3.3 --- Generalized Regularize gap function and Generalized D-gap function --- p.61 / Chapter 4 --- Error bound results for the merit functions --- p.74 / Chapter 4.1 --- Error bound results for Regularized gap function --- p.77 / Chapter 4.2 --- Error bound results for D-gap function --- p.78 / Chapter 4.3 --- Error bound results for Generalized Regularized gap function --- p.92 / Chapter 4.4 --- Error bound results for Generalized D-gap function --- p.93 / Bibliography --- p.105

Wang Xin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 61-63). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction and Literature Review --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- The Objective --- p.2 / Chapter 1.3 --- Literature Review --- p.3 / Chapter Chapter 2 --- The Model --- p.7 / Chapter Chapter 3 --- The Consistent Estimation of Chang-Point --- p.11 / Chapter 3.1 --- The Consistency of ιT --- p.11 / Chapter 3.2 --- The Case of Single Regressor --- p.15 / Chapter Chapter 4 --- The SupWald Test and Sample-Splitting Method --- p.20 / Chapter 4.1 --- The SupWald Test --- p.20 / Chapter 4.2 --- " The Distribution of WT (ι,0,1)" --- p.23 / Chapter 4.3 --- The Sample-Splitting Method --- p.25 / Chapter Chapter 5 --- Experimental Results --- p.27 / Chapter Chapter 6 --- Empirical Example --- p.41 / Chapter Chapter 7 --- Conclusion --- p.44 / Appendix --- p.46 / References --- p.61

Chan Ka Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 46-48). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Multiple comparison procedures and their applications --- p.1 / Chapter 1.2 --- Different types of error control --- p.3 / Chapter 1.3 --- Single-step and stepwise procedures --- p.5 / Chapter 1.4 --- From familywise error rate control to false discovery rate control --- p.8 / Chapter 1.5 --- The FDR procedure of BH --- p.10 / Chapter 1.6 --- Application of the FDR procedure --- p.11 / Chapter 1.7 --- Family size and family size robustness --- p.16 / Chapter 1.8 --- Objectives of the thesis --- p.17 / Chapter 2 --- The Familywise Robustness Criteria --- p.18 / Chapter 2.1 --- The basic idea of familywise robustness --- p.18 / Chapter 2.2 --- Definitions and notations --- p.19 / Chapter 2.3 --- The measurement of robustness to changing family size --- p.21 / Chapter 2.4 --- Main Theorems --- p.21 / Chapter 2.5 --- Example --- p.23 / Chapter 2.6 --- Summary --- p.24 / Chapter 3 --- FDR and FWR --- p.26 / Chapter 3.1 --- Positive false discovery rate --- p.26 / Chapter 3.2 --- A unified approach to FDR --- p.29 / Chapter 3.3 --- The S procedure --- p.30 / Chapter 3.4 --- Family wise robustness criteria and the S procedure --- p.32 / Chapter 4 --- Simulation Study --- p.41 / Chapter 4.1 --- The setup --- p.41 / Chapter 4.2 --- Simulation result --- p.43 / Chapter 4.3 --- Conclusions --- p.44 / Bibliography --- p.46

Zheng Xi Yin. / "December 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 117-121). / 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 Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

by Yang Weihong. / "March 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 89-92). / 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 Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Chan, Kin Kwok. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 68-69). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- The effect of using a default error model --- p.8 / Chapter 2.1 --- Formulae to measure the prediction error --- p.9 / Chapter 2.2 --- The effect of autoregressive parameter on SD of prediction error --- p.10 / Chapter 2.3 --- Misspecification error of SD of prediction error when using a default error model --- p.12 / Chapter 2.4 --- Reporting error of SD of prediction error when using a default error model --- p.23 / Chapter 3 --- Error modelling by using benchmarks --- p.30 / Chapter 3.1 --- Review of an existing method --- p.30 / Chapter 3.2 --- Introduction of Benchmark Forecasting Method --- p.32 / Chapter 3.3 --- Comparison of estimation methods --- p.36 / Chapter 4 --- Performance of using fitted error model --- p.41 / Chapter 4.1 --- Fitted value and reporting value of SD of prediction error when using a fitted error model --- p.41 / Chapter 4.2 --- Misspecification error and reporting error when using a fitted error model --- p.45 / Chapter 4.3 --- Suggestions on the selection of default and fitted error model --- p.51 / Chapter 5 --- Benchmarking performance of using fitted AR(1) model for usual ARMA survey error --- p.55 / Chapter 5.1 --- Model settings for two usual ARMA survey error --- p.56 / Chapter 5.2 --- Simulation studies --- p.57 / Chapter 6 --- An illustrative example: Traveller Accommodation series --- p.62 / Chapter 7 --- Conclusion --- p.66 / Bibliography --- p.68

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Survey data are often subject to a number of measurement errors. The measurement error associated with a multinomial variable is called a misclassification error. In this dissertation we study such errors when the outcome is binary. It is known that ignoring such misclassification errors may affect the parameter estimates, see for example Hausman, Abrevaya and Scott-Morton (1998). However, previous studies showed that robust estimation of the parameters is achievable if we take misclassification into account. There are many attempts to do so in the literature and the major problem in implementing them is to avoid poor or fragile identifiability of the misclassification probabilities. Generally we restrict these parameters by imposing prior information on them. Such prior constraints on the parameters are simple to impose within a Bayesian framework. Hence we consider a Bayesian logistic regression model that takes into account the misclassification of the dependent variable. A very convenient way to implement such a Bayesian analysis is to estimate the hierarchical model using the WinBUGS software package developed by the MRC biostatistics group, Institute of Public Health, at Cambridge University. WinGUGS allows us to estimate the posterior distributions of all the parameters using relatively little programming and once the program is written it is trivial to change the link function, for example from logit to probit. If we wish to have more control over the sampling scheme or to deal with more complex models, then we propose a data augmentation approach using the Metropolis-Hastings algorithm within a Gibbs sampling framework. The sampling scheme can be made more efficient by using a one-step Newton-Raphson algorithm to form the Metropolis-Hastings proposal. Results from empirically analyzing real data and from the simulation studies suggest that if suitable priors are specified for the misclassification parameters and the regression parameters, then logistic regression allowing for misclassification results in better estimators than the estimators that do not take misclassification into account.

Statisticians often focus on sampling or experimental design and data analysis while paying less attention to how the response is measured. However, the ideas of statistics may be applied to measurement problems with fruitful results. By examining the errors of measured responses, we may gain insight into the limitations of current measures and develop a better understanding of how to interpret and qualify the results. The first chapter considers the problem of measuring taxonomic richness as an index of habitat quality and stream health. In particular, we investigate numerical taxa richness (NTR), or the number of observed taxa in a fixed-count, as a means to assess differences in taxonomic composition and reduce cost. Because the number of observed taxa increases with the number of individuals counted, rare taxa are often excluded from NTR with smaller counts. NTR measures based on different counts effectively assess different levels of rarity, and hence target different parameters. Determining the target parameter that NTR is "really" estimating is an important step toward facilitating fair comparisons based on different sized samples. Our first study approximates the parameter unbiasedly estimated by NTR and explores alternatives for estimation based on smaller and larger counts. The second investigation considers response error resulting from panel evaluations. Because people function as the measurement instrument, responses are particularly susceptible to variation not directly related to the experimental unit. As a result, observed differences may not accurately reflect real differences in the products being measured. Chapter Two offers several linear models to describe measurement error resulting from unanchored responses across successive evaluations over time, which we call u-errors. We examine changes to Type I and Type II error probabilities for standard F-tests in balanced factorial models where u-errors are confounded with an effect under investigation. We offer a relatively simple method for determining whether or not distributions of mean square ratios for testing fixed effects change in the presence of u-error. In addition, the validity of the test is shown to depend both on the level of confounding and whether not u-errors vary about a nonzero mean. / Graduation date: 2002

We describe a method to solve the stereo correspondence using controlled eye (or camera) movements. These eye movements essentially supply additional image frames which can be used to constrain the stereo matching. Because the eye movements are small, traditional methods of stereo with multiple frames will not work. We develop an alternative approach using a systematic analysis to define a probability distribution for the errors. Our matching strategy then matches the most probable points first, thereby reducing the ambiguity for the remaining matches. We demonstrate this algorithm with several examples.