Ip Wing Yiu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaf 44). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Background --- p.1 / Chapter 1.3 --- Objective --- p.3 / Chapter 1.4 --- Scope of the thesis --- p.3 / Chapter 2 --- Basic Concepts --- p.5 / Chapter 2.1 --- Inverse Sampling --- p.5 / Chapter 2.2 --- Equivalence/ Non-inferiority Testing --- p.6 / Chapter 3 --- Inference for Risk Ratio --- p.8 / Chapter 3.1 --- Introduction --- p.8 / Chapter 3.2 --- Test Statistics for Risk Ratio --- p.8 / Chapter 3.3 --- Consistent Estimators of π --- p.12 / Chapter 4 --- Confidence Interval --- p.16 / Chapter 4.1 --- Introduction --- p.16 / Chapter 4.2 --- Tost-Based Confidence Interval --- p.17 / Chapter 4.3 --- Using sample-based estimates --- p.18 / Chapter 5 --- Simulation --- p.21 / Chapter 5.1 --- Introduction --- p.21 / Chapter 5.2 --- Simulation Procedures --- p.21 / Chapter 5.3 --- Simulation Results --- p.23 / Chapter 6 --- Conclusion --- p.27 / Appendix --- p.29 / Chapter A. --- Equation derviation --- p.29 / Chapter A1. --- Equation derviation 1 --- p.29 / Chapter A2. --- Equation derviation 2 --- p.31 / Chapter B. --- Table --- p.32 / References --- p.44

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The problem addressed is absence of a class of objects in a finite set of objects, which is investigated by considering absence of a species and absence in relation to a threshold. Regarding absence of a species, we demonstrate that the assessed probability of absence of the class of objects in the finite set of objects given absence of the class in the sample is either exactly or approximately equal to the probability of observing a specific single object from the class of objects given the protocol for observation, where probability is interpreted as a degree of belief. Regarding absence in relation to a threshold, we develop a new estimator of the upper confidence bound for the finite population distribution function evaluated at the threshold and investigate its properties for a set of finite populations. In addition we show that estimation regarding the initial ordered value in the finite population has limited usefulness. / Graduation date: 1998

Thesis (Ph. D.)--Oregon State University, 1967. / Typescript (photocopy). Includes bibliographical references (p. 89-93). Also available on the World Wide Web.

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (leaves 157-172).

Post stratification is considered desirable in sample surveys for two reasons - it reduces the mean squared error when averaged over all possible samples, and it reduces the conditional bias when conditioned on stratum sample sizes. The problem studied in this thesis is post stratified estimation of a finite population mean when there is a known auxiliary variable for each population unit. The primary direction of the thesis follows the lines of Holt and Smith (1979). A method is given for using the auxiliary variable in selection of the stratum boundaries and, using this approach to determine strata, to compare post stratified estimates with the self -weighting estimates from the analytical and empirical points of view. Estimates studied are: the post stratified mean, the post stratified combined ratio, and the post stratified separate ratio. The thesis contains simulation results that explore the distributions of the self -weighting estimates, and the post stratified estimates using conditional and unconditional inferences. The correct coverage properties of the confidence intervals are compared and the design effect, i.e. the ratio of the variance of the self -weighting to the variance of post stratified estimates, is calculated from the samples and its distribution explored by the simulation study for several real and artificial populations. The confidence intervals of post stratified estimates using conditional variances had good coverage properties for each sample configuration used, and hence the correct coverage property over all possible samples provided that the Central Limit Theorem was applied. The comparisons indicated that post stratification is an effective approach when the boundaries are obtained based on proper stratification using an auxiliary variable. Moreover it is more efficient than estimation based on simple random sampling in reducing the mean squared error. Finally, there is strong evidence that the post stratified estimates are robust against poorly distributed samples, whereas empirical investigations suggested that the self -weighting estimates are very poor when the samples are unbalanced. / Graduation date: 1990

Random processes are monitored over space and time by a network of stations distributed across a spatial region. Researchers have developed several analysis techniques to model the random process. Some of them require assumptions on the spatio-temporal variability of the process. An alternative method to analyze spatio-temporal data that does not require any assumption on the variance-covariance matrix is the Empirical Orthogonal Functions (EOF) model. The spatial distribution of the network sites influences the accuracy of the prediction results obtained by the EOF model. Researchers have proposed different methods to address this problem. We propose a model, the design-based EOF model, that incorporates information on the spatio-temporal variability of the process captured by the sampling design used to establish the network. The theoretical development of the model and an application are presented. We also consider the inclusion of auxiliary information into the design-based EOF model with the purpose of interpolating the process to unvisited sites. Interpolation results from the design-based EOF model are illustrated by considering a real data set and compared to spatial interpolation results obtained by using ordinary kriging. With the desire of making the design-based EOF model accessible to those monitoring programs that did not use a sampling probability design to establish the monitoring network, we consider two approaches that provide proper weights to be used in the model. / Graduation date: 2000

Thesis (M. Phil.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 66-70).

Thesis--Princeton University. / Cover title. "Reprinted from Annals of mathematical statistics, vol. XVII, no. 4, December, 1946." Bibliography: p. 408.

Thesis (Ph. D.)--University of Hong Kong, 1986.