published_or_final_version / abstract / Computer Science / Master / Master of Philosophy

Thesis (Ph. D.)--Oregon State University, 1981. / Typescript (photocopy). Includes bibliographical references (leaves 71-73). Also available via the World Wide Web.

In this paper we analyze how many shuffles are necessary to get close to ran- domness for a deck of n cards. Aldous (1983) shows that approximately 8.55 (n=52) shuffles are necessary when n is large. Bayer and Diaconis (1992) use the variation distance as a measure of randomness to analyze the most commonly used method of shuffling cards, and claim that 7 shuffles are enough when n=52. We provide another idea to measure the distance from randomness for repeated shuffles. The proposed method consists of a goodness of fit test and a simple simulation. Simulation results show that we have a similar conclusion to that of Bayer and Diaconis.

Thesis (M. Phil.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 127-132).

Thesis (Ph. D.)--York University, 2001. Graduate Programme in Statistics. / Typescript. Includes bibliographical references (leaves 96-103). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ66371.

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.