Thesis (M. Phil.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 82-91).

Copulas have been known in the statistical literature for many years, and have become useful tools in modeling dependence structure of multivariate random variables, overcoming some of the drawbacks of the commonly-used correlation measures. Goodness-of-fit tests for copulas play a very important role in evaluating the suitability of a potential input copula model. In recent years, many approaches have been proposed for constructing goodness-of-fit tests for copula families. Among them, the so-called “blanket tests" do not require an arbitrary data categorization or any strategic choice of weight function, smoothing parameter, kernel, and so on. As preliminaries, some background and related results of copulas are firstly presented. Three goodness-of-fit test statistics belonging to the blanket test classification are then introduced. Since the asymptotic distributions of the test statistics are very complicated, parametric bootstrap procedures are employed to approximate critical values of the test statistics under the null hypotheses. To assess the performance of the three test statistics in the low dependence cases, simulation studies are carried out for three bivariate copula families, namely the Gumbel-Hougaard copula family, the Ali-Mikhail-Haq copula family, and the Farlie-Gumbel-Morgenstern copula family. Specifically the effect of low dependence on the empirical sizes and powers of the three blanket tests under various combinations of null and alternative copula families are examined. Furthermore, to check the performance of the three tests for higher dimensional copulas, the simulation studies are extended to some three-dimensional copulas. Finally the three goodness-of-fit tests are applied to two real data sets. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

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

After defining the structure to a signal detection scheme, this dissertation describes and addresses some of the unresolved issues associated with its use when the interference encountered is impulsive. The alpha-stable (alpha-S) family of distributions is used as a model of this interference due to its physical interpretation and its general form. Despite its attractive features, difficulties arise in using this distribution due to, amongst other things, the lack of a general closed form expression for its probability density function. Relevant to the detection scheme used, this affects parameter estimation, signal detector design and goodness-of-fit tests. Significant contributions are made in the latter through the introduction of characteristic function based test that uses the parametric bootstrap. A modification of this test is then made to define a test of the level of impulsive behaviour - again the parametric bootstrap is employed to maintain levels of significance for this and another test based on testing the alpha-S parameter values. The performance of these tests is examined under simulated and two sources of real, impulsive data, namely human heart rate variability and fluctuations in stock prices. Once the appropriateness of the model assumption has been verified, the final, signal detection process may take place. Detectors based on the locally optimum criterion and approximations to it are described and compared to their rank-based counterparts. Results are presented that suggest compelling arguments based on performance and computational complexity for the consideration of rank-based techniques.Keywords: Impulsive behaviour, alpha-stable distribution, stable laws, Gaussianity testing, parameter estimation, goodness-of-fit, parametric bootstrap, signal detection, locally optimum detectors, rank-based detectors.

Assignment (MComm)--University of Stellenbosch, 2008. / Bibliography. Also available via the Internet.

Thesis (M.S.)--West Virginia University, 2006. / Title from document title page. Document formatted into pages; contains viii, 45 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 44-45).

Thesis (Ph.D.)--University of Toledo, 2005. / Typescript. "A dissertation [submitted] as partial fulfillment of the requirements of the Doctor of Philosophy degree in Mathematics." Bibliography: leaves 100-105.

Thesis (M. Phil.)--University of Hong Kong, 2005. / Title proper from title frame. Also available in printed format.

Judging goodness of fit in multidimensional scaling requires a comprehensive set of diagnostic tools instead of relying on stress rules of thumb. This article elaborates on corresponding strategies and gives practical guidelines for researchers to obtain a clear picture of the goodness of fit of a solution. Special emphasis will be placed on the use of permutation tests. The second part of the article focuses on goodness-of-fit assessment of an important variant of multidimensional scaling called unfolding, which can be applied to a broad range of psychological data settings. Two real-life data sets are presented in order to walk the reader through the entire set of diagnostic measures, tests, and plots. R code is provided as supplementary information that makes the whole goodness-of-fit assessment workflow, as presented in this article, fully reproducible.

Doctor of Philosophy / Department of Statistics / Shie-Shien Yang / Logistic regression model is a branch of the generalized linear models and is widely used in many areas of scientific research. The logit link function and the binary dependent variable of interest make the logistic regression model distinct from linear regression model. The conclusion drawn from a fitted logistic regression model could be incorrect or misleading when the covariates can not explain and /or predict the response variable accurately based on the fitted model- that is, lack-of-fit is present in the fitted logistic regression model. The current goodness-of-fit tests can be roughly categorized into four types. (1) The tests are based on covariate patterns, e.g., Pearson's Chi-square test, Deviance D test, and Osius and Rojek's normal approximation test. (2) Hosmer-Lemeshow's C and Hosmer-Lemeshow's H tests are based on the estimated probabilities. (3) Score tests are based on the comparison of two models, where the assumed logistic regression model is embedded into a more general parametric family of models, e.g., Stukel's Score test and Tsiatis's test. (4) Smoothed residual tests include le Cessie and van Howelingen's test and Hosmer and Lemeshow's test. All of them have advantages and disadvantages. In this dissertation, we proposed a partition logistic regression model which can be viewed as a generalized logistic regression model, since it includes the logistic regression model as a special case. This partition model is used to construct goodness-of- fit test for a logistic regression model which can also identify the nature of lack-of-fit is due to the tail or middle part of the probabilities of success. Several simulation results showed that the proposed test performs as well as or better than many of the known tests.