by Wai-sum Chan. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1986 / Includes bibliographical references.

by Tsz-Kit Keung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaf 81). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Testing Testable Hypotheses in Linear Models --- p.8 / Chapter 2.1 --- A General Theory --- p.9 / Chapter 2.2 --- The Method of Peixoto --- p.17 / Chapter 2.3 --- The Method of Chan and Li --- p.23 / Chapter Chapter 3 --- A New Method of Obtaining Equivalent Hypotheses --- p.32 / Chapter Chapter 4 --- Constrained Linear Models --- p.44 / Chapter 4.1 --- Hypothesis Testing in Constrained Linear Models --- p.44 / Chapter 4.2 --- Linear Models with Missing Observations --- p.50 / Chapter Chapter 5 --- Conclusions --- p.71 / Appendix --- p.74 / References --- p.81

Wong, Ka Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 46-49). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background --- p.4 / Chapter 2.1 --- Notation and Definitions --- p.4 / Chapter 2.2 --- Influence Function of β --- p.5 / Chapter 3 --- Methodology --- p.7 / Chapter 3.1 --- Robust Estimating Equations --- p.7 / Chapter 3.2 --- A General Algorithm for Robust GAM Estimation --- p.9 / Chapter 4 --- Asymptotic Equivalence --- p.12 / Chapter 5 --- Smoothing Parameter Selection --- p.16 / Chapter 5.1 --- Robust Cross-Validation --- p.17 / Chapter 5.2 --- Robust Information Criteria --- p.17 / Chapter 6 --- Multiple Covariates --- p.19 / Chapter 7 --- Simulation Study --- p.21 / Chapter 8 --- Real Data Examples --- p.26 / Chapter 8.1 --- Air Pollution Data --- p.26 / Chapter 8.2 --- Bronchitis Data --- p.28 / Chapter 9 --- Concluding Remarks --- p.31 / Chapter A --- Auxiliary Lemmas and Proofs --- p.32 / Chapter B --- Fisher Consistency Correction --- p.42 / Chapter B.1 --- Poisson distribution --- p.42 / Chapter B.2 --- Bernoulli distribution --- p.43 / Chapter C --- Derivation of (5.2) --- p.44 / Bibliography --- p.46

Mixed linear models are a time honored method of analyzing correlated data. However, there is still no method of calculating exact confidence intervals or p-values for an arbitrary parameter in any mixed linear model. Instead, researchers must use either specialized approximate and exact tests that have been developed for particular models or rely on likelihood based approximate tests and confidence intervals which may be unreliable in problems with small sample sizes. This thesis develops procedures to improve small sample likelihood based inference in these important models. The first manuscript develops I.M. Skovgaard's modified directed likelihood for mixed linear models and shows how it is a general, accurate, and easy to apply method of improving inference in mixed linear models. In the second manuscript, O.E. Barndorff-Nielsen's approximate modified profile likelihood is applied to mixed linear models. This modified profile likelihood is a sensible generalization of the commonly used residual likelihood and can be applied if either a fixed or a covariance parameter is of interest. The final manuscript discusses how the design of a mixed linear model effects the accuracy of Skovgaard's modified likelihood and suggests a useful decomposition of that statistic. / Graduation date: 1998

Geostatistical linear interpolation procedures such as kriging require knowledge of the covariance structure of the spatial process under investigation. In practice, the covariance of the process is unknown, and must be estimated from the available data. As the quality of the resulting predictions, and associated mean square prediction errors, depends on adequate specification of the covariance structure, it is important that the analyst be able to detect inadequacies in the specified covariance model. Case-deletion diagnostics are currently used by geostatisticians to evaluate spatial models. The second chapter of the thesis describes a particular case-deletion diagnostic based on standardized PRESS residuals, and its use in assessing the predictive capacity of spatial covariance models. Distributional properties of this statistic, denoted T [subscript PR], are discussed, and a saddlepoint approximation to its distribution is derived. Guidelines for calculating approximate p-values for the statistic under an hypothesized covariance model are also given. A simulation study demonstrates that the distributional and p-value approximations are accurate. The proposed method is illustrated through an example, and recommendations for calculation of T [subscript PR], and associated approximate p-values on a regional basis are given. The third chapter investigates the behavior of the standardized PRESS residuals under various misspecifications of the covariance matrix, V. A series of simulation studies show consistent patterns in the standardized PRESS residuals under particular types of misspecifications of V. It is observed that misspecification of V may lead to variability among the standardized PRESS residuals greater or less than would be expected if V was correctly specified, depending on the nature of the misspecification. Based on this observation, an adjustment to normal probability plots of the standardized PRESS residuals is proposed. The adjusted normal probability plots may be used to identify potential improvements to covariance models, without requiring extensive further calculations. / Graduation date: 1996

Thesis (Ph.D.)--York University, 2008. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 81-83). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR39029

Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (p. 170-182).

Not available / text

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

published_or_final_version / Statistics / Master / Master of Philosophy