Zugl.: Berlin, Humboldt-University, Habil.-Schr. / Lizenzpflichtig.

Viele Probleme der Kombinatorik, Zahlentheorie, Wahrscheinlichkeitstheorie, Zuverlässigkeitstheorie und Statistik lassen sich durch Anwendung einer einheitlichen Methode lösen, die als Prinzip der Inklusion-Exklusion bekannt ist. Das Prinzip der Inklusion-Exklusion drückt die Indikatorfunktion einer Vereinigung endlich vieler Ereignisse als alternierende Summe der Indikatorfunktionen ihrer Durchschnitte aus. Die vorliegende Schrift befasst sich mit verbesserten Inklusions-Exklusions-Identitäten und verbesserten Bonferroni-Ungleichungen, die voraussetzen, dass die Ereignisfamilie gewissen strukturellen Anforderungen genügt. Solche wohl-strukturierten Ereignisfamilien finden sich u.a. in der schließenden Statistik, der kombinatorischen Zuverlässigkeitstheorie und der chromatischen Graphentheorie. / Many problems in combinatorics, number theory, probability theory , reliability theory and statistics can be solved by applying a unifying method, which is known as the principle of inclusion-exclusion. The principle of inclusion-exclusion expresses the indicator function of a union of finitely many events as an alternating sum of indicator functions of their intersections. This thesis deals with improved inclusion-exclusion identities and improved Bonferroni inequalities that require the family of events to satisfy some structural restrictions. Examples of such well-structured families arise in problems of statistical inference, combinatorial reliability theory and chromatic graph theory.

Genome-wide Association (GWA) studies have become a widely used method for analyzing genetic data. It is useful in detecting associations that may exist between particular alleles and diseases of interest. This thesis investigates the dataset provided from problem 1 of the Genetic Analysis Workshop 16 (GAW 16). The dataset consists of GWA data from the North American Rheumatoid Arthritis Consortium (NARAC). The thesis attempts to determine a set of single nucleotide polymorphisms (SNP) that are associated significantly with rheumatoid arthritis. Moreover, this thesis also attempts to address the question of whether the one-sided alternative hypothesis that the minor allele is positively associated with the disease or the two-sided alternative hypothesis that the genotypes at a locus are associated with the disease is appropriate, or put another way, the question of whether examining both alternative hypotheses yield more information.

This dissertation considers quantile regression models with nonstationary or nearly nonstationary time series. The first chapter outlines the thesis and discusses its theoretical and empirical contributions. The second chapter studies inference in quantile regressions with cointegrated variables allowing for multiple structural changes. The unknown break dates and regression coefficients are estimated jointly and consistently. The conditional quantile estimator has a nonstandard limit distribution. A fully modified estimator is proposed to remove the second-order bias and nuisance parameters and the resulting limit distribution is mixed normal. A simulation study shows that the fully modified quantile estimator has good finite sample properties. The model is applied to stock index data from the emerging markets of China and several mature markets. Financial market integration is found in some quantiles of the Chinese stock indices. The third chapter considers predictive quantile regression with a nearly integrated regressor. We derive nonstandard distributions for the quantile regression estimator and t-statistic in terms of functionals of diffusion processes. The critical values are found to depend on both the quantile of interest and the local-to-unity parameter, which is not consistently estimable. Based on these critical values, we propose a valid Bonferroni bounds test for quantile predictability with persistent regressors. We employ this new methodology to test the ability of many commonly employed and highly persistent regressors, such as the dividend yield, earnings price ratio, and T-bill rate, to predict the median, shoulders, and tails of the stock return distribution. Chapter Four proposes a cumulated sum (CUSUM) test for the null hypothesis of quantile cointegration. A fully modified quantile estimator is adopted for serial correlation and endogeneity corrections. The CUSUM statistic is composed of the partial sums of the residuals from the fully modified quantile regression. Under the null, the test statistic converges to a functional of Brownian motions. In the application to U.S. interest rates of different maturities, evidence in favor of the expectations hypothesis for the term structure is found in the central part of the distributions of the Treasury bill rate and financial commercial paper rate, but in the tails of the constant maturity rate distribution. / Thesis (Ph.D, Economics) -- Queen's University, 2012-07-30 15:20:38.253

Humboldt-Univ., Habil.-Schr.--Berlin. / Literaturverz. S. [100] - 109.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

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The role of surface chemical effects in hydraulic fracturing of shale is studied using the results of unconfined compression tests and Brazilian tests on Mancos shale- cored at depths of 20-60 ft. The rock mineralogy, total organic carbon and cation exchange capacity were determined in order to characterize the shale. Adsorption tests to study the interaction of the shale and aqueous fluid mixture were also carried out using surface tension measurements. The uniaxial compressive strengths and tensile strengths of individual shale samples after four hours exposure to water, 2.85 x 10^-3 M cationic surfactant (dodecyltrimethylammonium bromide-DTAB) and 2.81 x 10^-3 M anionic surfactant (sodium dodecylbenzenesulfonate-SDBS) were analyzed using ANOVA and Bonferroni tests. These mechanical strengths were largely reduced on exposure to the aqueous environments studied, despite the relatively low clay and low swelling clay content of the Mancos shale. Further comparison of the uniaxial compressive strengths and tensile strengths of the shale on exposure to water, to the strengths when exposed to the surfactant solutions showed that their difference was not statistically significant indicating that exposure to water had the greatest effect on strength loss. The surface tension measurement of 2.85 x 10^-4 M DTAB and 2.81 x 10^-4 M SDBS solutions before and after equilibration with shale showed about 80% increase in surface tension in the DTAB solution and 10% increase in surface tension in the SDBS solution. The probable sorption mechanism is electrostatic attraction with negatively charged sites of the shale as shown by significant loss of the cationic surfactant (DTAB) to the shale surface, and the relatively minor adsorption capacity of the anionic surfactant (SDBS). Although these adsorption tests indicate interaction between the shale and surfactant solutions, within the number of tests carried out and the surfactant concentration used, the interaction does not translate into a significant statistical difference for impacts of surfactants on mechanical strength of this shale compared to the impact of water alone. The relevance of this work is to facilitate the understanding of how the strength of rock can be reduced by the composition of hydraulic fracturing fluids, to achieve improved fracture performance and higher recovery of natural gas from shale reservoirs.

Introduction: The aim of this in vitro study was to determine the influence of two glide path preparation methods on the fracture rate of the Primary 25/08 WaveOne reciprocating instrument. The number of simulator Endo-Training-Blocks in each group were calculated at the time of instrument fracture and compared to determine the influence of glide path preparation on the failure rate of the Primary 25/08 WaveOne reciprocating instrument. Preparation times for different glide path methods and total time for root canal preparation, with or without glide path, was also calculated. Materials and Methods: Simulator Endo-Training-Blocks (n = 300) were selected and randomly divided into 3 groups (n = 100). The 3 groups were then sub-divided into 5 smaller groups (n = 20). Root canal preparation was done with new primary 25/08 WaveOne instruments allocated to each group (5 in total for each group, 1 for each sub-group) following different methods for glide path preparation. Group 1: no glide path (control); Group 2: glide path preparation with stainless-steel hand files (size 10 K-File followed by size 15 K-File and finally size 20 K-File until loose fitting); and Group 3: glide path preparation with rotary PathFiles (size 10 K-File until loose fitting followed by PathFile no.1 (ISO 13 tip), PathFile no.2 (ISO 16 tip) and finally PathFile no. 3 (ISO 19 tip)). The Primary 25/08 WaveOne reciprocating instrument was used with the WaveOne endodontic motor in “WaveOne All “mode with a brushing motion on the outstroke. Simulated root canals were irrigated with sterile water and Glyde was used as lubricating agent. The outcome was measured by recording how many simulators could be prepared with one instrument before instrument breakage occurred. The preparation protocol was repeated 5 times. The time it took to prepare the glide path and the total preparation time was also calculated. The data of the different parts of the project were collected and statistically analysed using the ANOVA / Bonferroni test. Results: Glide path preparation with PathFiles was significantly faster (13.3 s ± 2.60 s) than with hand files (25.1 s ± 1.70 s) (P < 0.001). The highest number of simulators could be prepared after glide path preparation was performed with PathFiles (19.2 ± 0.84) (P < 0.001). Pairwise comparisons at the Bonferroni adjusted significance level of 0.017 demonstrated that there were statistical significant differences (P < 0.001) when PathFiles (19.2 ± 0.84) and hand files (17.6 ±1.14) were compared to the no glide path group (7.4 ± 0.89). There was no statistical significant difference between PathFiles and hand files groups. Total Preparation time was significantly shorter (P < 0.001) when an initial glide path was prepared with PathFiles (12.7 ± 0.22 s). The longest preparation time (P < 0.001) was calculated in group 1 where no glide path (21.2 ± 0.20 s) was present and the Endo-Training-Blocks were left undisturbed. Conclusion: Initial glide path preparation with PathFiles resulted in shorter preparation time (glide path and total preparation) and allowed a higher number of simulators prepared before failure of the WaveOne instrument. / Dissertation (MSc)--University of Pretoria, 2013. / gm2014 / Odontology / unrestricted

O objetivo deste trabalho é estudar a performance de alguns métodos de comparações múltiplas (MCMs) que ajustam o valor-p quando as estatísticas empregadas nos testes são a log-rank e a Cramér-von Mises, ambas não paramétricas e com estrutura de dependência. A vantagem dos MCMs que ajustam o valor-p é que eles controlam as taxas de erro tipo I e tipo II para cada hipótese, afim de atingir um poder estatístico elevado, mantendo a taxa de erro da família dos testes (FWER) menor ou igual ao nível de significância escolhido. Trabalhamos com o procedimento clássico de Bonferroni e com outros métodos vistos como seu melhoramento, com especial atenção a certos procedimentos derivados do método de Simes que permitem realizar inferências sob as hipóteses individuais. Foi verificado teoricamente que a estatística log-rank pertence à classe multivariada totalmente positiva de ordem 2 (\'MTP IND. 2\'), uma vez que o método de Simes garante o controle da FWER quando as estatísticas dependentes assumem esta condição. O controle da FWER empregando a estatística de Cramér-von Mises foi observado apenas por meio de simulações. Os MCMs foram analisados através de estudos computacionais em modelos discretos e contínuos sob censura com foco no problema de comparar um tratamento versus controle / The aim of this work is to study the performance of some Multiple Comparison Methods (MCMs) that adjust the p-value when the log-rank-type and Cramér-von Mises statistics are used, both nonparametric and with dependency structure. The advantage of these methods is that they control the error rates of type I and type II for each hypothesis in order to achieve high statistical power while keeping the Family Wise Error Rate (FWER) lower or equal than a given significance level. The classical Bonferroni procedure is used as well as others seen as its improvement, with special attention to certain procedures derived from Simes\' method for making inferences on individual hypothesis. It is theoretically proved that the weighted Log-Rank statistics belongs to the multivariate totally positive of order 2 (\'MTP IND. 2\') class, which is needed in order to apply Simes\' method, that guarantees control of the FWER of dependent statistics in this case. The control of the FWER when the Cramér-von Mises statistics is used is only veried by means of computational simulations. The MCMs are also analyzed by means of computational experiments with discrete and continuous data under censoring with focus on the problem of comparisons of treatment versus a control