Chan For Yee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 88-90). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Basic Concepts --- p.6 / Chapter 2.1 --- Binomial vs Inverse Sampling --- p.6 / Chapter 2.2 --- Equivalence / Non-inferiority Test --- p.7 / Chapter 3 --- Testing Procedures --- p.9 / Chapter 3.1 --- The Model --- p.9 / Chapter 3.2 --- Asymptotic Behaviors of the Estimators --- p.10 / Chapter 3.2.1 --- Asymptotic Test Statistic based on Unconditional Maximum Likelihood Estimate --- p.12 / Chapter 3.2.2 --- Asymptotic Test Statistic based on restricted maximum likelihood estimate --- p.13 / Chapter 3.3 --- Conditional Exact Procedures --- p.16 / Chapter 3.3.1 --- Non-test-statistic-based procedure --- p.17 / Chapter 3.3.2 --- Test-statistic-based procedure --- p.17 / Chapter 4 --- Simulation Study --- p.19 / Chapter 4.1 --- Simulation Results - Type I error rate --- p.21 / Chapter 4.1.1 --- Asymptotic Test Statistic based on Unconditional MLE . . --- p.21 / Chapter 4.1.2 --- Asymptotic Test Statistic based on Restricted MLE . . . . --- p.22 / Chapter 4.1.3 --- Non-test-statistic-based Conditional Exact Test --- p.23 / Chapter 4.1.4 --- Test-statistic-based Conditional Exact Test --- p.24 / Chapter 4.2 --- Simulation Results - Power --- p.25 / Chapter 4.2.1 --- Asymptotic Tests - Similarity and Difference between using Unconditional and Restricted MLE --- p.25 / Chapter 4.2.2 --- Conditional Exact Tests - Similarity and Difference be- tween using Non-test-statistic-based and Test-statistic-based Procedures --- p.30 / Chapter 4.2.3 --- Test-statistic-based Conditional Exact Tests - Similarity and Difference between using Unconditional and Restricted MLE --- p.31 / Chapter 5 --- Conclusion --- p.32 / Appendices --- p.36 / Chapter A. --- Simulation Result - Type I error rate --- p.36 / Chapter B. --- Simulation Result - Power value --- p.42 / Bibliography --- p.88

Lee Ka-ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 68-70). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Multiple Test Procedure --- p.7 / Chapter 2.1 --- Hypothesis Test for Individual Centre --- p.8 / Chapter 2.2 --- Multiple Hypothesis Test for Multi-Centre --- p.11 / Chapter 2.2.1 --- Single-step Multiple Test Procedure --- p.11 / Chapter 2.2.2 --- Sequentially Rejective Multiple Test Procedure --- p.12 / Chapter 2.2.3 --- Multiple Test Procedure for Discrete Distribution --- p.14 / Chapter 2.2.4 --- Summary of various Multiple Test Procedures --- p.17 / Chapter 3 --- Simulation Study --- p.19 / Chapter 3.1 --- Comparisons of Sizes --- p.19 / Chapter 3.1.1 --- Based on Asymptotic Approach --- p.22 / Chapter 3.1.2 --- Based on Exact Approach --- p.23 / Chapter 3.1.3 --- Based on Mid-P Approach --- p.25 / Chapter 3.1.4 --- "Comparisons between Asymptotic, Exact and Mid-P Approaches" --- p.26 / Chapter 3.2 --- Comparisons of Power --- p.29 / Chapter 3.2.1 --- Based on Asymptotic Approach --- p.32 / Chapter 3.2.2 --- Based on Exact Approach --- p.33 / Chapter 3.2.3 --- Based on Mid-P Approach --- p.33 / Chapter 3.2.4 --- Asymptotic vs. Exact Approaches --- p.34 / Chapter 3.2.5 --- Exact vs. Mid-P Approaches --- p.34 / Chapter 3.2.6 --- Asymptotic vs. Mid-P Approaches --- p.34 / Chapter 4 --- Illustrative Examples --- p.36 / Chapter 5 --- Conclusions and Discussions --- p.43 / Figures --- p.45 / References --- p.68

Cheung, Ka Wai Ricker. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 68-69). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Basic Concepts --- p.1 / Chapter 1.2 --- Linkage Disequilibrium --- p.5 / Chapter 1.3 --- Transmission Disequilibrium Test --- p.7 / Chapter 1.4 --- Scope of Thesis --- p.8 / Chapter 2 --- Transmission Disequilibrium Test --- p.9 / Chapter 2.1 --- The Model --- p.9 / Chapter 2.2 --- The Data Structure and The Statistic --- p.12 / Chapter 3 --- Small Sample Properties of Transmission Disequilibrium Test --- p.16 / Chapter 3.1 --- Exact Distribution of TDT Statistic --- p.16 / Chapter 3.2 --- Power under Alternative Hypothesis --- p.20 / Chapter 3.3 --- P-Value --- p.29 / Chapter 4 --- Exact P-Value and Power --- p.35 / Chapter 5 --- Haplotype Relative Risk --- p.61 / Chapter 6 --- Conclusion --- p.66 / References --- p.68

Thesis (Ph. D.)--State University of New York at Binghamton, Dept. of Mathematical Sciences, 2006. / Includes bibliographical references.

This dissertation concerns two topics in the analysis of finite population surveys: setting sample size and hypothesis testing. The first concerns the a priori determination of the sample size needed to obtain species members. The second concerns testing distributional hypotheses when two equal-size populations are sampled. Setting sample size to obtain species is a problem which arises when an investigator wants to obtain (1) a member of all species present in an area (2) a member of all species whose relative frequency is greater than, say, 20% or (3) a member of each species in a target set of species. Chapter 2 presents a practical solution to these questions by setting a target sample size for which the species are obtained with known probability. The solution requires the estimated relative frequency of the rarest species of interest; total number of species is not needed. Because this problem has substantial computational demands, easy-to-compute formulas are needed and given. Three practical examples are presented. Testing of finite population distributional hypotheses is covered in Chapter 3. The test proposed here works under reasonably general designs and is based on a Horvitz-Thompson type correction of the usual Mann-Whitney U statistic. The investigation here compared this proposed test to a corrected (for finiteness) form of the usual Wilcoxon rank sum test. Size and power of the two test procedures are investigated using simulation. The proposed test had approximately correct nominal size over a wide range of situations. The corrected Wilcoxon test exhibited extreme violations in size in many cases. Power of the two tests in situations where they have equal size is similar in most practically interesting cases. / Graduation date: 1996

Thesis (Ph. D.)--University of California, San Diego, 2003. / Vita. Includes bibliographical references.

Infections frequently occur on both networks of devices and networks of people, and can model not only viruses, but also information, rumors, and product use. However, in many circumstances, the infection process itself is hidden, and only the effects, e.g. sickness or knowledge, can be observed. In addition, this information is likely incomplete, missing many sick nodes, as well as inaccurate, with false positives. To use this data effectively, it is often essential to identify the infection process causing the sickness, or even whether the cause is an infection. For our purposes, we consider the susceptible-infected (SI) infection model. We seek to distinguish between infections and random sickness, as well as between different infection (or infection-like) processes in a limited information setting. We formulate this as a hypothesis testing problem, where (typically) in the null, the sickness affects nodes at random, and in the alternative, the infection is spread through the network. Similarly, we consider the case where the sickness may be caused by one of two infection (or infection-like) processes, and we wish to find which is the causative process. We do this is a setting with very limited information, given only a single snapshot of the infection. Only a small portion of the infected population reports the sickness. In addition, there are several other limitations we consider. There may be false positives, obfuscating the infection. Similarly, there may be a random sickness and epidemic process occurring simultaneously. Knowledge of the graph topology may be incomplete, with unknown edges over which the infection may spread. The graph may also be weighted, affecting the way the infection spreads over the graph. In all these cases, we develop algorithms to identify the causative process of the infection utilizing the fact that infected nodes will be clustered. We demonstrate that under reasonable conditions, these algorithms detect an infection with asymptotically zero error probability as the graph size increases. / text

published_or_final_version / abstract / Statistics and Actuarial Science / Master / Master of Philosophy

No description available.

In statistical inference one of the most important properties that an estimator of an unknown parameter can possess is the property of sufficiency. The use of sufficient statistics has been prescribed in the past and their use today plays an ever increasing role in modern statistical inference. Because of the utmost importance of sufficient statistics, it is the goal of this thesis to study the various aspects of sufficiency in connection with the estimation of parameters.This study utilizes a blend of a geometric and an analytic approach to sufficiency. This is done to show the power of each and to demonstrate how the two approaches complement each other and combine to give better insight into the concept of sufficiency.In this thesis the author also establishes some new and important results on sufficiency and minimal sufficiency. These results, taken as a whole, constitute a unified presentation of some of the most important aspects of sufficiency and non-sufficiency.