Detecting a change in the structure of a time series is a classical statistical problem. Here we consider a short memory causal linear process $X_i=\sum_{j=0}^\infty a_j\xi_{i-j}$, $i=1,\cdots,n$, where the innovations $\xi_i$ are independent and identically distributed and the coefficients $a_j$ are summable. The goal is to detect the existence of an unobserved time at which there is a change in the marginal distribution of the $X_i$'s. Our model allows us to simultaneously detect changes in the coefficients and changes in location and/or scale of the innovations. Under very simple moment and summability conditions, we investigate the asymptotic behaviour of the sequential empirical process based on the $X_i$'s both with and without a change-point, and show that two proposed test statistics are consistent. In order to find appropriate critical values for the test statistics, we then prove the validity of the moving block bootstrap for the sequential empirical process under both the hypothesis and the alternative, again under simple conditions. Finally, the performance of the proposed test statistics is demonstrated through Monte Carlo simulations.

Change is an organizational inevitability. There are few fields that undergo change more rapidly than information technology. Keeping up with the pace of change in a field so inclined toward change may take a unique toll on workers in information technology. Yet, little has been done to investigate workers' orientations towards change in this turbulent field. Accordingly, this research explores attitudes toward change and some possible related characteristics among individuals who work in the field of information technology. The primary purpose of this study is to explore the nature of resistance to change in information technology. The secondary purpose of this study was to discover potential relationships between resistance to change and several well known motivational variables; specifically empowerment, engagement, and workaholism. Trust was included in this model as well because it has been shown to relate to both motivation and resistance to change and because trust is generally understood to be a characteristic that eases interaction and reduces transaction costs. This study used a web-based survey to collect responses from individuals employed in two medium-sized information technology organizations. Responses were analyzed using correlational, regression, path, and factor analyses to analyze participants' responses. Results indicated that resistance to change is a factor in information technology. Also, two of three motivational characteristics related negatively to resistance to change. Trust related negatively to resistance to change and positively to the same two motivational characteristics, but did not mediate the relationship between these variables. These findings are discussed in terms of their relevance to the study of information technology as they suggest possible implications for organizational functioning, individual well-being, technology adoption, and coping, and innovation.

Advances in computing has undoubtfully been one of the main catalysts in the formation of the discipline always known as Statistics. A fundamental question addressed here is whether computing facilities, such as parallel or high performance computing, could assist in the development of methodologies that render stronger results, based on some predetermined optimality criterion. The candidate at the hand of which this enquiry is made, is the arc length of some statistical function. Estimation, goodness-of-fit, linear regression and non-linear regression, which may all be considered as central themes in Statistics, are revisited, and redefined in terms of this new measure. The results resulting from these arc length methodologies are obtained from simulation, as well as from real case studies, and contrasted to that obtained using their classical counterparts. Mathematical premises for the proposed methods are provided, together with the documentation accompanying the companion R package, along with the data utilised for the applications. / Thesis (PhD)--University of Pretoria, 2017. / National Research Foundation of South Africa, Unique Grant No. 94108. / Statistics / PhD / Unrestricted

Loving God is our highest perfection for Leibniz. It secures our belief and trust in the Creator, which is integral to the sciences as well as faith. Those who love God have justification for reasoning, that is, they can rationally expect to arrive at truth. This is because love is a receptivity to the perfection all of things; loving God, then, is a disposition and tendency toward the most perfect being, the ens perfectissimum. Individuals who perceive the divine nature “do not merely fear the power of the supreme and all-seeing monarch,” Leibniz writes, “but are assured of his beneficence, and lastly—and what brings everything together—burn with a love of God above all else.”1 In my dissertation, I argue that Leibniz’s qualification should be taken seriously: love of God “brings everything together.” The subject of my dissertation can be stated schematically. It consists of two pairs of claims, one pair philosophical, the other theological: A moral quality is required to secure our reason. From a most perfect unity, a moral quality follows. Love of God is our highest perfection. Love of God secures our reasoning. Both concern the security of reason, by which I mean the rational motivation for reasoning itself. They are reasons we ought to expect reasoning to lead to truth. Yet they do not form a tight demonstration: while an inference is clearly at work in the first pair, there are no inferences in the second. Also, there is a distinction between a moral quality and love for God. Unless they are identified, Leibniz’s philosophy and theology secure reasoning apart from one another. In 1686, Leibniz wrote his well-known “Discourse on Metaphysics.” A few months after, he composed a theological treatise, Examination of the Christian Religion. These texts, I argue, should be read side by side, and the first chapter compares how divine perfection secures our reasoning in both texts. Some Moderns’ notion of perfection—namely, Descartes’, Spinoza’s, and Malebranche’s—fail to secure our reasoning because their views entail arbitrariness in the world and the divine nature. But a proper sense of perfection, one that includes a moral quality, secures our reasoning by ensuring that everything is amenable to reason. Descartes also sought to secure our reasoning, and for the second and third chapters I compare his account with Leibniz’s own, then draw out the latter’s criticisms. For Descartes, the deity’s moral quality is characterized by an indifferent will, which is eminently and formally revealed throughout creation. Although recognizing the infinite source of all things directs our attention appropriate in the Cartesian system, Leibniz criticizes Descartes’ detached and indifferent God. When our disposition toward God is not characterized by love, we are less rational than otherwise. Leibniz finds intolerable moral implications in the Cartesian system, and I work out these implications in chapter three. Descartes’ criteria of true and false ideas does not settle dispute, but relies on “interior testimony.” Proper reasoning, then, does not tend toward unity among persons, and this is especially problematic in religious debate. Descartes’ method is Stoic, which also leads to trouble when it comes to church unity: one remains in the church by a sheer act of will, which can violate reason. Leibniz views such a detachment of faith and reasoning as dangerous, besides impoverishing the concept of reason altogether. Leibniz’s notions of God and perfection secure our reason by engendering love for God. “Discourse” and Examen begin with a moral disposition and tendency. In the last chapter, I argue that this is the case by considering two criteria Leibniz adopts—his test for perfection and the kinds of knowledge—as well as the foundation of his logic at the time. Leibniz can tolerate provisional beginnings, hypothetical truths, and original sin because of his robust conception of love. He distinguishes two ways we love God: spes, or hope, is a disposition or tendency to natural perfection, and caritas, or esteem, affection, or love, regards divine perfection. These states orient us according to the divine plan. Miracles are within the world as an effect of the deity’s moral quality: they are a means God personally relates to rational beings. Miracles reveal the moral effects of our perception of phenomena generally, included the regularity observed and classified by science. So, to conclude, I compare Leibniz’s discussion of revelation in Examen with his discussion of miracles in “Discourse” to draw out the significance of miracles for him. Besides much debate on the implications of miracles for his conception of substance, I argue that there is a moral motivation for retaining miracles, even those of the second rank.

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Magister Artium (Psychology) - MA(Psych) / While research into children’s subjective well-being (SWB) has advanced over the past decade, there is a paucity of cross-cultural research, particularly in South Africa. Moreover, while the adaptation and validation of instruments in English and Afrikaans are evident, other language groups have not received much attention. This study aimed to provide structural validation of the Students’ Life Satisfaction Scale across a sample of children in South Africa using multi-group analysis across three language groups (Setswana, Xitsonga, and Tshivenda). Within this process, the study aimed to use multi-group confirmatory factor analysis (MGCFA) to compare the structural validity and measurement invariance of the three language groups. Finally, the study aimed to determine the convergent validity of the three language groups of the SLSS by regressing them onto the single-item Overall Life Satisfaction Scale (OLS). The study uses data from Wave 3 of the South African Children’s Worlds Study and included a sample of 625 children across the language groups (Setswana: n = 187; Sesotho: n = 170; and Tshivenda: n = 268). For the overall pooled sample an excellent fit was obtained for a single-factor model, including one error-covariance. Standardised regression weights of the items ranged between .43 and .73. MGCFA revealed an acceptable fit for the configural model (unconstrained loadings); however, metric (constrained loadings) and scalar invariance (constrained loadings and intercepts) was not tenable. However, through the application of partial constraints metric invariance was tenable when Item 5 (I like my life) was freely estimated, while scalar invariance was tenable when Item 1 (I enjoy my life) and Item 5 (I like my life) were freely estimated. The results suggest that the Items: My life is going well; I have a good life; The things in my life are excellent; and I am happy with my life, are comparable by correlations, regression coefficients, and latent mean scores across the three language groups. Convergent validity using the OLS was obtained for the pooled sample and across the language groups. The key contribution of the study is establishing that the Setswana, Sesotho, and Tshivenda translated and adapted versions of the SLSS are valid for use within the South African context to measure children’s SWB, and that they can be grouped together in an overall pooled sample.

Integration in the European Union (EU) in terms of the legal as well as economic spheres has grown in depth, scope and speed since its establishment. The EU has significantly affected various fields of policies within its member states, including the environment. This is understood as the 'Europeanisation process'. The Netherlands, considered one of the pioneering countries to establish environmental measures, has approximately 80% of its legislation in the environmental field derived from European legislation. The thesis seeks to answer how Dutch environmental policy has been affected by the EU over the past twenty years. The implementation process of three environmental directives is analysed concerning water, biodiversity and air, to understand this process. The concept of Europeanisation and the related theory of goodness of fit is applied to argue that the implementation process of European environmental directives in the Netherlands is effective if there are no major adjustments necessary in the national setting, i.e. there is no policy or institutional misfit between domestic and European legislation, and no veto players impede the process. On the other hand, the implementation process is significantly more complicated if the directive needs extensive transformations. It is concluded that...

In many hypothesis testing problems such as one-sample and two-sample test problems, the test statistics are degenerate U-statistics. One of the challenges in practice is the computation of U-statistics for a large sample size. Besides, for degenerate U-statistics, the limiting distribution is a mixture of weighted chi-squares, involving the eigenvalues of the kernel of the U-statistics. As a result, it’s not straightforward to construct the rejection region based on this asymptotic distribution. In this research, we aim to reduce the computation complexity of degenerate U-statistics and propose an easy-to-calibrate test statistic by using the divide-and-conquer method. Specifically, we randomly partition the full n data points into kn even disjoint groups, and compute U-statistics on each group and combine them by averaging to get a statistic Tn. We proved that the statistic Tn has the standard normal distribution as the limiting distribution. In this way, the running time is reduced from O(n^m) to O( n^m/km_n), where m is the order of the one sample U-statistics. Besides, for a given significance level , it’s easy to construct the rejection region. We apply our method to the goodness of fit test and two-sample test. The simulation and real data analysis show that the proposed test can achieve high power and fast running time for both one and two-sample tests.

This dissertation compares the parameter estimates obtained from two item response theory (IRT) models: the 1-PL IRT model and the MC1-PL IRT model. Several scenarios were explored in which both unidimensional and multidimensional item-level and personal-level data were used to generate the item responses. The Monte Carlo simulations mirrored the real-life application of the two correlated dimensions of Necessary Operations and Calculations in the basic mathematics domain. In all scenarios, the MC1-PL IRT model showed greater precision in the recovery of the true underlying item difficulty values and person theta values along each primary dimension as well as along a second general order factor. The fit statistics that are generally applied to the 1-PL IRT model were not sensitive to the multidimensional item-level structure, reinforcing the requisite assumption of unidimensionality when applying the 1-PL IRT model.