It is well known that the generation of random vectors with non-independent components is difficult. Nevertheless, we propose a new and very simple generation algorithm for multivariate linear densities over point-symmetric domains. Among other applications it can be used to design a simple decomposition-rejection algorithm for multivariate concave distributions. / Series: Research Report Series / Department of Statistics and Mathematics

We introduce computationally efficient Monte Carlo methods for studying the statistics of stochastic differential equations in two distinct settings. In the first, we derive importance sampling methods for data assimilation when the noise in the model and observations are small. The methods are formulated in discrete time, where the "posterior" distribution we want to sample from can be analyzed in an accessible small noise expansion. We show that a "symmetrization" procedure akin to antithetic coupling can improve the order of accuracy of the sampling methods, which is illustrated with numerical examples. In the second setting, we develop "stochastic continuation" methods to estimate level sets for statistics of stochastic differential equations with respect to their parameters. We adapt Keller's Pseudo-Arclength continuation method to this setting using stochastic approximation, and generalized least squares regression. Furthermore, we show that the methods can be improved through the use of coupling methods to reduce the variance of the derivative estimates that are involved.

This diploma thesis deals with the importance of tourism for a group of states which includes Portugal, Spain, Italy and Greece. The aim of this thesis is to identify the importance of tourism to the economy and to interconnect it with the competitiveness of those countries in tourism via an analysis of the current situation in tourism and via analysing the effects that tourism has on these economies in the past last five years. The first chapter explains the most important terms concerning the subject in theory. The next chapter introduces tourism within the PIGS economies and the third chapter is devoted to tourism competitiveness of the southern EU countries and creates a predicition of their future development in tourism.

Bancos de dados oriundos de processos industriais são caracterizados por elevado número de variáveis correlacionadas, dados ruidosos e maior número de variáveis do que observações, tornando a seleção de variáveis um importante problema a ser analisado no monitoramento de tais processos. A presente dissertação propõe sistemáticas para seleção de variáveis com vistas à classificação de bateladas produtivas. Para tanto, sugerem-se novos métodos que utilizam Índices de Importância de Variáveis para eliminação sistemática de variáveis combinadas a ferramentas de classificação; objetiva-se selecionar as variáveis de processo com maior habilidade discriminante para categorizar as bateladas em classes. Os métodos possuem uma sistematização básica que consiste em: i) separar os dados históricos em porções de treino e teste; ii) na porção de treino, gerar um Índice de Importância de Variáveis (IIV) que ordenará as variáveis de acordo com sua capacidade discriminante; iii) a cada iteração, classificam-se as amostras da porção de treino e removem-se sistematicamente as variáveis; iv) avaliam-se então os subconjuntos através da distância Euclidiana dos resultados dos subconjuntos a um ponto hipotético ótimo, definindo assim o subconjunto de variáveis a serem selecionadas. Para o cumprimento das etapas acima, são testadas diferentes ferramentas de classificação e IIV. A aplicação dos métodos em bancos reais e simulados verifica a robustez das proposições em dados com distintos níveis de correlação e ruído. / Databases derived from industrial processes are characterized by a large number of correlated, noisy variables and more variables than observations, making of variable selection an important issue regarding process monitoring. This thesis proposes methods for variable selection aimed at classifying production batches. For that matter, we propose new methods that use Variable Importance Indices for variable elimination combined with classification tools; the objective is to select the process variables with the highest discriminating ability to categorize batch classes. The methods rely on a basic framework: i) split historical data into training and testing sets; ii) in the training set, generate a Variable Importance Index (VII) that will rank the variables according to their discriminating ability; iii) at each iteration, classify samples from the training set and remove the variable with the smallest VII; iv) candidate subsets are then evaluated through the Euclidean distance to a hypothetical optimum, selecting the recommended subset of variables. The aforementioned steps are tested using different classification tools and VII’s. The application of the proposed methods to real and simulated data corroborates the robustness of the propositions on data with different levels of correlation and noise.

It is well known that for highly skewed distributions the standard method of using the t statistic for the confidence interval of the mean does not give robust results. This is an important problem for importance sampling (IS) as its final distribution is often skewed due to a heavy tailed weight distribution. In this paper, we first explain Hall's transformation and its variants to correct the confidence interval of the mean and then evaluate the performance of these methods for two numerical examples from finance which have closed-form solutions. Finally, we assess the performance of these methods for credit risk examples. Our numerical results suggest that Hall's transformation or one of its variants can be safely used in correcting the two-sided confidence intervals of financial simulations.(author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Responding to the changes in the insurance environment of the past decade, insurance regulators globally have been revamping the valuation and capital regulations. This thesis is concerned with the design and analysis of statistical inference procedures that are used to implement these new and upcoming insurance regulations, and their analysis in a more general setting toward lending further insights into their performance in practical situations. The quantitative measure of risk that is used in these new and upcoming regulations is the risk measure known as the Tail Value-at-Risk (T-VaR). In implementing these regulations, insurance companies often have to estimate the T-VaR of product portfolios from the output of a simulation of its cash flows. The distributions for the underlying economic variables are either estimated or prescribed by regulations. In this situation the computational complexity of estimating the T-VaR arises due to the complexity in determining the portfolio cash flows for a given realization of economic variables. A technique that has proved promising in such settings is that of importance sampling. While the asymptotic behavior of the natural non-parametric estimator of T-VaR under importance sampling has been conjectured, the literature has lacked an honest result. The main goal of the first part of the thesis is to give a precise weak convergence result describing the asymptotic behavior of this estimator under importance sampling. Our method also establishes such a result for the natural non-parametric estimator for the Value-at-Risk, another popular risk measure, under weaker assumptions than those used in the literature. We also report on a simulation study conducted to examine the quality of these asymptotic approximations in small samples. The Haezendonck-Goovaerts class of risk measures corresponds to a premium principle that is a multiplicative analog of the zero utility principle, and is thus of significant academic interest. From a practical point of view our interest in this class of risk measures arose primarily from the fact that the T-VaR is, in a sense, a minimal member of the class. Hence, a study of the natural non-parametric estimator for these risk measures will lend further insights into the statistical inference for the T-VaR. Analysis of the asymptotic behavior of the generalized estimator has proved elusive, largely due to the fact that, unlike the T-VaR, it lacks a closed form expression. Our main goal in the second part of this thesis is to study the asymptotic behavior of this estimator. In order to conduct a simulation study, we needed an efficient algorithm to compute the Haezendonck-Goovaerts risk measure with precise error bounds. The lack of such an algorithm has clearly been noticed in the literature, and has impeded the quality of simulation results. In this part we also design and analyze an algorithm for computing these risk measures. In the process of doing we also derive some fundamental bounds on the solutions to the optimization problem underlying these risk measures. We also have implemented our algorithm on the R software environment, and included its source code in the Appendix.

Background: In recent years, interest towards Corporate Social Responsibility (CSR) has increased, more specifically, the economic, environmental, and social impacts large corporations have on society. This has led to the increase in transparency of practices in CSR disclosure, and number of sustainability reports published in general. In particular, the automotive industry has proved to be quite unsustainable, and is heavily focusing on its sustainable impacts. Purpose: The purpose of the study is to answer why practices in CSR disclosure are an increasingly important phenomena, and more specifically, why companies engage in them. This is done by having Volvo Cars as a case study and analyzing its annual and sustainability reports for the years from 2018 to 2020. Method: The framework used to analyze the results is Carroll’s pyramid of CSR, and thus, examining four dimensions of CSR: economic, legal, ethical, and philanthropic. The results were further analyzed through stakeholder theory, in order to distinguish which practices in CSR disclosure were aimed at affecting the company’s primary, secondary, and both primary and secondary stakeholders, respectively, and conclude why companies in the automotive industry engage in CSR. Conclusion: The conclusions of the study are that Volvo Cars is a company, which heavily emphasizes on its sustainable activities and aims at achieving a competitive advantage via its practices in CSR disclosure, by affecting all stakeholder groups. Thus, the reason practices in CSR disclosure are becoming increasingly important is because companies see it as a means of positioning themselves in today’s highly competitive environment, and thus, achieving a competitive advantage.

While the Arab Spring has resulted in numerous different political outcomes across the Arab world, conventional theories of democratization are lacking in explaining these divergent outcomes. Developing a theory of democratization, strategic importance and external intervention, I examine the relationship between national strategic importance and democratization. I argue that strategically important states will be targeted by external actors in attempts to stifle or thwart democracy because democracy may upset the status quo that foreign actors benefit from. I do not find support for the hypothesis that strategic importance and democratization share a general negative relationship, however, I find moderate support that strategic importance is related to the timing of regime breakdown, democratic breakdown and democratic transition. Furthermore, in examining the cases of Bahrain, Egypt, Tunisia and Libya, I highlight key moments of external intervention and influence that impacted the democratization attempts of each case.

The Diploma thesis deals with the analysis of Human Resources Department processes with a view to increasing its importance and effectiveness. In the theoretical part the point at issue is outlined as seen both from the point of view of experts from real business and quoted literature. The practical part focuses on the study of personnel managers´ activities and HR department processes. In the final analysis based on the research having been carried out some recommendations are suggested for the company.

This study sought to find out if there is a correlation between the wellbeing and work performance of Christian managers and support from their families. Based on Don Browning’s revised correlation approach to practical theology, the study employed a mixed methods research design (quantitative and qualitative). This study involved an empirical study with thirty-two (32) Christian managers in Ohangwena Region, Namibia. The participants in the empirical study either completed a questionnaire or participated in an interview. Additionally, six biblical leaders and other key scriptures were selected to draw theological principles related to Christian managers’ wellbeing and work performance in relation to family support. The results revealed that Christian managers’ experiences at work, at home and at church affect their physical, emotional, psychological, social and spiritual wellbeing; wellbeing affects the work performance of Christian managers, family support plays a significant role in the wellbeing and work performance of Christian managers; most Christian managers do receive support from their families, but families can do much more; Christian managers have a role to play in gaining support from their families; the church has a part to play in enhancing family support to address the wellbeing needs and work performance of Christian managers. Based on the findings, the study culminated in the designing of a model to enhance the wellbeing and work performance of Christian managers, which can be used by Christian managers, Christian managers’ families and Christian practitioners such as pastors and counsellors. Osmer’s four tasks of practical theology were found to be especially useful for pastoral intervention. / Thesis (PhD)--University of Pretoria, 2018. / University of Pretoria / Practical Theology / PhD / Unrestricted