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

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

In the study of multiple comparisons tests the following topics were discussed: (i) extension to the general case of certain properties and results which previously had been given for three and four means only, (ii) power vectors and average power, (iii) expressions of power for the multiple range tests and for the multiple F test involving only three means, and (iv) methods for evaluating power. These four topics are amplified in order in the four paragraphs below. A set of recursion formulas was obtained for enumerating the decision patterns for n means. x_i was given by the equation See: Equation where i = 1, 2,...,n-1. In IV, formulas were derived which express d_j,i+1 as a function of the x_i. This made possible the writing of the bounding equations for any decision region involving n means. The regions (1,2), (1,2,3), (1,2,4), ..., (1,2....,n) for the multiple range tests were described in the sample-space of differences among n means. / Ph. D.

The study seeks to determine the degree of accumulation of Type II error rates, while violating the assumptions of normality, for different specified levels of power among sample means. The study employs a Monte Carlo simulation procedure with three different specified levels of power, methodologies, and population distributions. On the basis of the comparisons of actual and observed error rates, the following conclusions appear to be appropriate. 1. Under the strict criteria for evaluation of the hypotheses, Type II experimentwise error does accumulate at a rate that the probability of accepting at least one null hypothesis in a family of tests, when in theory all of the alternate hypotheses are true, is high, precluding valid tests at the beginning of the study. 2. The Dunn-Bonferroni procedure of setting the critical value based on the beta value per contrast did not significantly reduce the probability of committing a Type II error in a family of tests. 3. The use of an adequate sample size and orthogonal contrasts, or limiting the number of pairwise comparisons to the number of means, is the best method to control for the accumulation of Type II errors. 4. The accumulation of Type II error is irrespective of distributions.

In this thesis, we focus on the the comparison of treatments with ordered categorical responses. The three cases of treatment comparisons will all be studied. The main objective of this thesis is to develop more effective comparison methods for treatments with ordinal responses and to address some important issues involved in different comparison problems. Our major statistical approach is to consider ordinal responses as manifestations of some underlying continuous random variables. / The comparison of treatments to detect possible treatment effects is a very important topic in statistical research. It has been drawing significant interests from both academicians and practitioners. Important research work on treatment comparisons dates back several decades. For treatment comparisons, the following three cases are very common: the comparison of two independent treatments; the comparison of treatments with repeated measurements; and the multiple comparison of several treatments. For different cases, the involved research issues are usually different. In many fields of study, the level of measurement for responses of the treatments is ordinal. Many examples can be found in areas such as biostatistics, psychology, sociology, and market research, where the ordered categorical variables play an important role. / This thesis consists of three main parts. In the first part, we consider the modeling of treatments with longitudinal ordinal responses by a latent growth curve. On the basis of such a latent growth curve, we achieve a comprehensive flexible model with straightforward interpretations and a variety of applications including treatment comparison, the analysis of covariates, and equivalence test of treatments. In the second part, we consider the comparison of several treatments with a control for ordinal responses. By considering the ordinal responses as manifestations of some underlying normal random variables, a latent normal distribution model is utilized and the corresponding parameter estimation method is proposed. Further, we also derive testing procedures that compare several treatments with a control under an analytical framework. Both single-step and stepwise procedures are introduced, and these procedures are compared in terms of average power based on a simulation study. In the last part of this thesis, we establish a unified framework for treatment comparisons with ordinal responses, which allows various treatment comparison methods be comprehended using a unified perspective. The latent variable model is also utilized, but the underlying random variables are allowed to have any member of the location-scale distribution family. This latent variable model under such a specification of underlying distributions subsumes many existing models in the literature. A two-step procedure to identify the model and produce the parameter estimates is proposed. Based on this procedure, many important statistical inferences can be conveniently conducted. Furthermore, the sample size determination method based on the latent variable method is also proposed. The proposed latent variable method is compared with the existing methods in terms of power and sample size. / Lu, Tongyu. / Adviser: Wai-Yin Poon. / Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 94-101). / 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, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Graduation date: 1994

published_or_final_version / Statistics / Doctoral / Doctor of Philosophy

Thesis (Ph. D.)--University of Hong Kong, 1990.

Thesis (Ph.D.)--Ohio University, August, 2009. / Title from PDF t.p. Includes bibliographical references.

Thesis (Ph.D.) -- University of Rhode Island, 2008. / Typescript. Includes bibliographical references (leaves 104-113).