Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The Beta-Skew-t-EGARCH model was recently proposed in literature to model the volatility of financial returns. The inferences over the model parameters are based on the maximum likelihood method. The maximum likelihood estimators present good asymptotic properties; however, in finite sample sizes they can be considerably biased. Monte Carlo simulations were used to evaluate the finite sample performance of point estimators. Numerical results indicated that the maximum likelihood estimators of some parameters are biased in sample sizes smaller than 3,000. Thus, bootstrap bias correction procedures were considered to obtain more accurate estimators in small samples. Better quality of forecasts was observed when the model with bias-corrected estimators was considered. In addition, we propose a likelihood ratio test to assist in the selection of the Beta-Skew-t-EGARCH model with one or two volatility components. The numerical evaluation of the two-component test showed distorted null rejection rates in sample sizes smaller than or equal to 1,000. To improve the performance of the proposed test in small samples, the bootstrap-based likelihood ratio test and the bootstrap Bartlett correction were considered. The bootstrap-based test exhibited the closest null rejection rates to the nominal values. The evaluation results of the two-component tests showed their practical usefulness. Finally, an application to the log-returns of the German stock index of the proposed methods was presented. / O modelo Beta-Skew-t-EGARCH foi recentemente proposto para modelar a volatilidade de retornos financeiros. A estimação dos parâmetros do modelo é feita via máxima verossimilhança. Esses estimadores possuem boas propriedades assintóticas, mas em amostras de tamanho finito eles podem ser consideravelmente viesados. Com a finalidade de avaliar as propriedades dos estimadores, em amostras de tamanho finito, realizou-se um estudo de simulações de Monte Carlo. Os resultados numéricos indicam que os estimadores de máxima verossimilhança de alguns parâmetros do modelo são viesados em amostras de tamanho inferior a 3000. Para obter estimadores pontuais mais acurados foram consideradas correções de viés via o método bootstrap. Verificou-se que os estimadores corrigidos apresentaram menor viés relativo percentual. Também foi observada melhor qualidade das previsões quando o modelo com estimadores corrigidos são considerados. Para auxiliar na seleção entre o modelo Beta-Skew-t-EGARCH com um ou dois componentes de volatilidade foi apresentado um teste da razão de verossimilhanças. A avaliação numérica do teste de dois componentes proposto demonstrou taxas de rejeição nula distorcidas em tamanhos amostrais menores ou iguais a 1000. Para melhorar o desempenho do teste foram consideradas a correção bootstrap e a correção de Bartlett bootstrap. Os resultados numéricos indicam a utilidade prática dos testes de dois componentes propostos. O teste bootstrap exibiu taxas de rejeição nula mais próximas dos valores nominais. Ao final do trabalho foi realizada uma aplicação dos testes de dois componentes e do modelo Beta-Skew-t-EGARCH, bem como suas versões corrigidas, a dados do índice de mercado da Alemanha.

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In an attempt to prove Amitsur's Conjecture for cyclic subgroups of the Brauer group, we look at rational embeddings of the Severi Brauer variety of an algebra into its norm hypersurface. We enlarge the collection of such embeddings, and generalize them to embeddings of generalized Severi Brauer varieties into determinantal varieties. / text

In model-based clustering mixture models are used to group data points into clusters. A useful concept introduced for Gaussian mixtures by Malsiner Walli et al. (Stat Comput 26:303-324, 2016) are sparse finite mixtures, where the prior distribution on the weight distribution of a mixture with K components is chosen in such a way that a priori the number of clusters in the data is random and is allowed to be smaller than K with high probability. The number of clusters is then inferred a posteriori from the data. The present paper makes the following contributions in the context of sparse finite mixture modelling. First, it is illustrated that the concept of sparse finite mixture is very generic and easily extended to cluster various types of non-Gaussian data, in particular discrete data and continuous multivariate data arising from non-Gaussian clusters. Second, sparse finite mixtures are compared to Dirichlet process mixtures with respect to their ability to identify the number of clusters. For both model classes, a random hyper prior is considered for the parameters determining the weight distribution. By suitable matching of these priors, it is shown that the choice of this hyper prior is far more influential on the cluster solution than whether a sparse finite mixture or a Dirichlet process mixture is taken into consideration.

This thesis explores the problems of fitting antedependence (AD) models and partial antecorrelation (PAC) models to continuous non-Gaussian longitudinal data. AD models impose certain conditional independence relations among the measurements within each subject, while PAC models characterize the partial correlation relations. The models are parsimonious and useful for data exhibiting time-dependent correlations. Since the relation of conditional independence among variables is rather restrictive, we first consider an autoregressively characterized PAC model with independent asymmetric Laplace (ALD) innovations and prove that this model is an AD model. The ALD distribution previously has been applied to quantile regression and has shown promise for modeling asymmetrically distributed ecological data. In addition, the double exponential distribution, a special case of the ALD, has played an important role in fitting symmetric finance and hydrology data. We give the distribution of a linear combination of independent standard ALD variables in order to derive marginal distributions for the model. For the model estimation problem, we propose an iterative algorithm for the maximum likelihood estimation. The estimation accuracy is illustrated by some numerical examples as well as some longitudinal data sets. The second component of this dissertation focuses on AD multivariate skew normal models. The multivariate skew normal distribution not only shares some nice properties with multivariate normal distributions but also allows for any value of skewness. We derive necessary and sufficient conditions on the shape and covariance parameters for multivariate skew normal variables to be AD(p) for some p. Likelihood-based estimation for balanced and monotone missing data as well as likelihood ratio hypothesis tests for the order of antedependence and for zero skewness under the models are presented. Since the class of skew normal random variables is closed under the addition of independent standard normal random variables, we then consider an autoregressively characterized PAC model with a combination of independent skew normal and normal innovations. Explicit expressions for the marginals, which all have skew normal distributions, and maximum likelihood estimates of model parameters, are given. Numerical results show that these three proposed models may provide reasonable fits to some continuous non-Gaussian longitudinal data sets. Furthermore, we compare the fits of these models to the Treatment A cattle growth data using penalized likelihood criteria, and demonstrate that the AD(2) multivariate skew normal model fits the data best among those proposed models.

<p>A container crane of STS-type, Ship To Shore, consists of a spreader hanging underneath a railrunning trolly. As the container is under the influence of wind, it is likely that it starts to turn in a torsional pendulum. This report handles how the torsional pendulum of a container crane can be damped. </p><p>A number of different models have been developed to analyze how different placement of the actuators affects the system. Two differens types of controllers, LQG and MPC, have been developed and applied to these models. The different models and controlers were evaluated and compared by studying simulation results in timedomain. Moreover in order to make the simulations more realistic, a wind model has been developed and applied. </p><p>The models and controllers have been analyzed with bodediagrams and sensitivity functions. </p><p>The analyses shows clearly that the best placement of the actuators for control of the torsional pendulum on an STS-crane is in the trolly, pulling and relaxing the wires. This control is best handled by a state feedback control (LQG). Furthermore, the control should in this way, with addition of in the horizontalplane movable suspensions in the trolly, work acceptably in the whole operational area of a STS-crane.</p>

A container crane of STS-type, Ship To Shore, consists of a spreader hanging underneath a railrunning trolly. As the container is under the influence of wind, it is likely that it starts to turn in a torsional pendulum. This report handles how the torsional pendulum of a container crane can be damped. A number of different models have been developed to analyze how different placement of the actuators affects the system. Two differens types of controllers, LQG and MPC, have been developed and applied to these models. The different models and controlers were evaluated and compared by studying simulation results in timedomain. Moreover in order to make the simulations more realistic, a wind model has been developed and applied. The models and controllers have been analyzed with bodediagrams and sensitivity functions. The analyses shows clearly that the best placement of the actuators for control of the torsional pendulum on an STS-crane is in the trolly, pulling and relaxing the wires. This control is best handled by a state feedback control (LQG). Furthermore, the control should in this way, with addition of in the horizontalplane movable suspensions in the trolly, work acceptably in the whole operational area of a STS-crane.

Clock synchronization between any two nodes in a Wireless Sensor Network (WSNs) is generally accomplished through exchanging messages and adjusting clock offset and skew parameters of each node’s clock. To cope with unknown network message delays, the clock offset and skew estimation schemes have to be reliable and robust in order to attain long-term synchronization and save energy. A joint clock offset and skew estimation scheme is studied and developed based on the Gaussian Mixture Kalman Particle Filter (GMKPF). The proposed estimation scheme is shown to be a more flexible alternative than the Gaussian Maximum Likelihood Estimator (GMLE) and the Exponential Maximum Likelihood Estimator (EMLE), and to be a robust estimation scheme in the presence of non-Gaussian/nonexponential random delays. This study also includes a sub optimal method called Maximum Likelihood-like Estimator (MLLE) for Gaussian and exponential delays. The computer simulations illustrate that the scheme based on GMKPF yields better results in terms of Mean Square Error (MSE) relative to GMLE, EMLE, GMLLE, and EMLLE, when the network delays are modeled as non-Gaussian/non-exponential distributions or as a mixture of several distributions.

The construction of horizontally curved bridges with skewed supports requires careful consideration. These types of bridges exhibit three-dimensional response characteristics that are not commonly seen in straight bridges with normal supports. As a result, engineers may face difficulties during the construction, when the components of the bridge do not fit together or the final geometry of the structure does not correspond to that intended by the designer. These complications can lead to problems that compromise the serviceability aspects of the bridge and in some cases, its structural integrity. The three dimensional response that curved and skewed bridges exhibit is directly influenced by the bracing system used to configure the structure. In I-girder bridges, cross-frames are provided to integrate the structure, transforming the individual girders into a structural system that can support larger loads than when the girders work separately. In general, they facilitate the construction of the structure. However, they can also induce undesired collateral effects that can be a detriment to the performance of the system. These effects must be considered in the design of a curved and skewed bridge because, in some cases, they can modify substantially its response. This research is focused on understanding how the bracing system affects the performance of curved and skewed I-girder bridges, as well as, the ability of the approximate analysis methods to capture the structural behavior. In this research, techniques that can be implemented in the creation of 2D-grid models are developed to overcome the limitations of this analysis method. In addition, efficient cross-frame arrangements that mitigate the collateral effects of skew are developed. These mitigation schemes reduce the undesired cross-frame forces and flange lateral bending stresses associated with the transverse stiffness of the structure, while ensuring that the bracing system still performs its intended functions.

The SHIRA method of Mehrmann and Watkins belongs among the structure preserving Krylov subspace methods for solving skew-Hamiltonian eigenvalue problems. It can also be applied to Hamiltonian eigenproblems by considering a suitable transformation. Structure induced shift-and-invert techniques are employed to steer the algorithm towards the interesting region of the spectrum. However, the shift cannot be altered in the middle of the computation without discarding the information that has been accumulated so far. This paper shows how SHIRA can be combined with ideas from Ruhe's Rational Krylov algorithm to yield a method that permits an adjustment of shift after every step of the computation, adding greatly to the flexibility of the algorithm. We call this new method rational SHIRA. A numerical example is presented to demonstrate its efficiency.