Thesis (M. Phil.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 95-101).

Thesis (M.S.)--University of West Florida, 2009. / Title from title page of source document. Document formatted into pages; contains 80 pages. Includes bibliographical references.

Thesis--University of Washington. / Vita. Another copy has number: Thesis 27614. Bibliography: leaves [152]-155.

In many areas of research, such as within medical statistics, biology and geostatistics, problems arise requiring the analysis of angular (or directional) data. Many possess experimental design problems and require analysis of variance techniques for suitable analysis of the angular data. These techniques have been developed for very limited cases and the sensitivity of such techniques to the violation of assumptions made, and their possible extension to larger experimental models, has yet to be investigated. The general aim of this project is therefore to develop suitable experimental design models and analysis of variance type techniques for the analysis of directional data. Initially a generalised linear modelling approach is used to derive parameter estimates for one-way classification designs leading to maximum likelihood methods. This approach however, when applied to larger experimental designs is shown to be intractable due to optimization problems. The limited analysis of variance techniques presently available for angular data are reviewed and extended to take account of the possible addition of further factors within an experimental design. These are shown to breakdown under varying conditions and question basic underlying assumptions regarding the components within the original approach. A new analysis of variance approach is developed which possesses many desirable properties held in standard 'linear' statistical analysis of variance. Finally several data sets are analysed to support the validity of the new techniques.

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Measures of data quality are important for the evaluation and improvement of survey design and procedures. A detailed investigation of the sources, magnitude and impact of errors is necessary to identify how survey design and procedures may be improved and how resources allocated more efficiently among various aspects of the survey operation. A major part of this thesis is devoted to the overview of statistical theory and methods for measuring the contribution of response variability to the overall error of a survey. A very common practice in surveys is to select groups (clusters) of elements together instead of independent selection of elements. In practice cluster samples tend to produce higher sampling variance for statistics than element samples of the same size. Their frequent use stems from the desirable cost features that they have. Most data collection and sample designs involve some overlapping between interviewer workload and the sampling units (clusters). For those cases, a proportion of the measurement variance, which is due to interviewers, is reflected to some degree in the sampling variance calculations. The prime purpose in this thesis is to determine a variance formula that decomposes the total variance into sampling and measurement variance components for two commonly used data collection and sample designs. Once such a decomposition is obtained, determining an optimum allocation in existence of measurement errors would be possible.

Abstract This thesis presents methods for modelling conditional variance and uncertainty of prediction at a query point on the basis of industrial process data. The introductory part of the thesis provides an extensive background of the examined methods and a summary of the results. The results are presented in detail in the original papers. The application presented in the thesis is modelling of the mean and variance of the mechanical properties of steel plates. Both the mean and variance of the mechanical properties depend on many process variables. A method for predicting the probability of rejection in a quali?cation test is presented and implemented in a tool developed for the planning of strength margins. The developed tool has been successfully utilised in the planning of mechanical properties in a steel plate mill. The methods for modelling the dependence of conditional variance on input variables are reviewed and their suitability for large industrial data sets are examined. In a comparative study, neural network modelling of the mean and dispersion narrowly performed the best. A method is presented for evaluating the uncertainty of regression-type prediction at a query point on the basis of predicted conditional variance, model variance and the effect of uncertainty about explanatory variables at early process stages. A method for measuring the uncertainty of prediction on the basis of the density of the data around the query point is proposed. The proposed distance measure is utilised in comparing the generalisation ability of models. The generalisation properties of the most important regression learning methods are studied and the results indicate that local methods and quadratic regression have a poor interpolation capability compared with multi-layer perceptron and Gaussian kernel support vector regression. The possibility of adaptively modelling a time-varying conditional variance function is disclosed. Two methods for adaptive modelling of the variance function are proposed. The background of the developed adaptive variance modelling methods is presented.

Tree-ring series that record climatic variation have long been of interest for study of possible effects of solar variability on terrestrial phenomena. Spectral analysis, harmonic dial analysis, digital filtering, cross-correlation and principal component analysis were used separately and in combination in an attempt to detect relationships between the annual Wolf sunspot numbers and ring-width indices, primarily from western North America. The results show no evidence of significant, consistent relationships between tree-ring data and sunspot numbers.