Thesis (M.S.)--University of North Carolina at Wilmington, 2005. / Includes bibliographical references (leaves: 52-55)

Thesis (Ph.D.) - University of Queensland, 2006. / Includes bibliography.

Thesis (M.A.)--University of North Carolina at Wilmington, 2006. / Includes bibliographical references (leaf: 24)

Orientador: Edson Denis Leonel / Banca: Iberê Luiz Caldas / Banca: Tiago Pereira da Silva / Resumo: Estudamos nessa dissertação algumas propriedades estatísticas no regime de equilibrio pós transitório para o modelo bouncer unidimensional considerando ambas versões completa e simplificada. O modelo consiste de uma partícula clássica movendo-se sob ação de uma força gravitacional constante e sofrendo colisões com uma plataforma móvel de massa muito maior que a massa da partícula. A versão completa leva em conta o movimento real da fronteira e o instante da colisão entre partícula e plataforma é obtido a partir da solução numérica de uma equação transcendental. Já o modelo simplificado, também conhecido como modelo de aproximação de fronteira fixa, assume que para o cálculo do instante da colisão a fronteira está parada, porém a partícula troca energia após a colisão ocorre como se a fonteira estivesse em movimento. Os comportamentos da velocidade média, velocidade quadrática média e desvio da velocidade quadrática média foram obtidos em função dos parâmetros de controle. Desenvolvemos um método semi-analítico permitindo-nos deduzir equações dos valores médios sem fazer simulações de larga escala. Em seguida, elaboramos uma simulação do tipo Monte-Carlo que nos permite obter os valores médios no estado estacionário sem resolver equações transcendentais, acelerando assim as simulações numéricas. O método de Monte-Carlo apresentado pode ser útil na investigação de sistemas mais complexos incluindo bilhares clássicos dependentes do tempo / Abstract: We studied some statistical properties in the stationary and post transitory state for the one-dimensional bouncer model considering wither complete and simplified versions. The model consists of a classical particle moving under the effect of a constant gravitational force and collides with a periodic moving platform whose mass is heavier as compared to the particle. The complete version takes into account the real motion of the moving wall. The instant of collision is obtained from the numerical solution of a transcendental equation. The simplified version, also called as a static wall approximation, takes into account to calculate the instant of the collisions as if the wall was fixed. However, the particle experiences an exchange of energy and momentum at the collision as if the wall were moving. The behavior for the average velocity, average squared velocity and deviation of the average squared velocity were obtained as a function of the control parameters. We developed a semi-analytic method allowing us to deduce equations for the average values without the need of doing large scale simulations. Using a Monte-Carlo-like simulation we obtained the average values for the stationary state without solving the transcendental equations. The Monte-Carlo method may have applications in the investigation of more complex systems including time dependent billiard systems / Mestre

In this Thesis we explore the problem of structural alignment of protein molecules using statistical shape analysis techniques. The structural alignment problem can be divided into three smaller ones: the representation of protein structures, the sampling of possible alignments between the molecules and the evaluation of a given alignment. Previous work done in this field, can be divided in two approaches: an adhoc algorithmic approach from the Bioinformatics literature and an approach using statistical methods either in a likelihood or Bayesian framework. Both approaches address the problem from a different scope. For example, the algorithmic approach is easy to implement but lacks an overall modelling framework, and the Bayesian address this issue but sometimes the implementation is not straightforward. We develop a method which is easy to implement and is based on statistical assumptions. In order to asses the quality of a given alignment we use a size and shape likelihood density which is based in the structure information of the molecules. This likelihood density is also extended to include sequence infor- mation and gap penalty parameters so that biologically meaningful solution can be produced. Furthermore, we develop a search algorithm to explore possible alignments from a given starting point. The results suggest that our approach produces better or equal alignments when it is compared to the most recent struc- tural alignment methods. In most of the cases we managed to achieve a higher number of matched atoms combined with a high TMscore. Moreover, we extended our method using Bayesian techniques to perform alignments based on posterior modes. In our approach, we estimate directly the mode of the posterior distribution which provides the final alignment between two molecules. We also, choose a different approach for treating the mean parameter. In previous methods the mean was either integrated out of the likelihood density or considered as fixed. We choose to assign a prior over it and obtain its posterior mode. Finally, we consider an extension of the likelihood model assuming a Normal density for both the matched and unmatched parts of a molecule and diagonal covariance structure. We explore two different variants. In the first we consider a fixed zero mean for the unmatched parts of the molecules and in the second we consider a common mean for both the matched and unmatched parts. Based on simulated and real results, both models seems to perform well in obtaining high number of matched atoms and high TMscore.

Most of the notations and terminological conventions used in this thesis are Statistical. The aim in risk management is to describe the risk factors present in time series. In order to group these risk factors, one needs to distinguish between different stochastic processes and put them into different classes. The risk factors discussed in this thesis are fat tails and mean reversion. The presence of these risk factors fist need to be found in the historical dataset. I will refer to the historical dataset as the original dataset. The Ljung- Box-Pierce test will be used in this thesis to determine if the distribution of the original dataset has mean reversion or no mean reversion. / Mathematical Sciences / M.Sc. (Applied Mathematics)

Orientador: Verónica Andrea González-Lopez / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-18T10:24:16Z (GMT). No. of bitstreams: 1 Schultz_JoseAdolfodeAlmeida_M.pdf: 781903 bytes, checksum: 6f13c49a1d8a278498ea105b9b9a7a31 (MD5) Previous issue date: 2011 / Resumo: O resumo poderá ser visualizado no texto completo da tese digital / Abstract: The abstract is available with the full electronic digital document / Mestrado / Inferencia Bayesiana / Mestre em Estatística

Orientador: Filidor Edilfonso Vilca Labra / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-05T23:55:16Z (GMT). No. of bitstreams: 1 Zeller_CamilaBorelli_M.pdf: 3683998 bytes, checksum: 26267086098b12bd76b1d5069f688223 (MD5) Previous issue date: 2006 / Resumo: Neste trabalho, apresentamos um estudo de inferência estatística no modelo de Grubbs em grupos, que representa uma extensão do modelo proposto por Grubbs (1948,1973) que é freqüentemente usado para comparar instrumentos ou métodos de medição. Nós consideramos a parametrização proposta por Bedrick (2001). O estudo é baseado no método de máxima verossimilhança. Testes de hipóteses são considerados e baseados nas estatísticas de wald, escore e razão de verossimilhanças. As estimativas de máxima verossimilhança do modelo de Grubbs em grupos são obtidas usando o algoritmo EM e considerando que as observações seguem uma distribuição normal. Apresentamos um estudo de análise de diagnóstico no modelo de Grubbs em grupos com o interesse de avaliar o impacto que um determinado subgrupo exerce na estimativa dos parâmetros. Vamos utilizar a metodologia de influência local proposta por Cook (1986), considerando o esquema de perturbação: ponderação de casos. Finalmente, apresentamos alguns estudos de simulação e ilustramos os resultados teóricos obtidos usando dados encontrados na literatura / Abstract: In this work, we presented a study of statistical inference in the Grubbs's model with subgroups, that represents an extension of the model proposed by Grubbs (1948,1973) that is frequently used to compare instruments or measurement methods. We considered the parametrization proposed by Bedrick (2001). The study is based on the maximum likelihood method. Tests of hypotheses are considered and based on the wald statistics, score and likelihood ratio statistics. The maximum likelihood estimators of the Grubbs's model with subgroups are obtained using the algorithm EM and considering that the observations follow a normal distribution. We also presented a study of diagnostic analysis in the Grubb's model with subgroups with the interest of evaluating the effect that a certain one subgroup exercises in the estimate of the parameters. We will use the methodology of local influence proposed by Cook (1986) considering the schemes of perturbation of case weights. Finally, we presented some simulation studies and we illustrated the obtained theoretical results using data found in the literature / Mestrado / Mestre em Estatística

Orientador: Luiz Koodi Hotta / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T03:56:46Z (GMT). No. of bitstreams: 1 Sakamoto_CarolinedeFreitas_M.pdf: 4538610 bytes, checksum: 977f3115a7248c40284073adc86889ac (MD5) Previous issue date: 2012 / Resumo: A construção de distribuições multivariadas com dependências assimétricas, especialmente com dependências complexas nas caudas, é um requisito necessário em muitas aplicações, particularmente em finanças. A teoria de cópulas pode ser bastante útil nesta tarefa. Neste sentido, algumas das propostas sugeridas na literatura são os modelos hierárquicos arquimedianos, os modelos pair-cópula e a cópula t-Student assimétrica. Esta dissertação está focada no estudo e aplicação de modelos de cópulas com dimensões maiores que três através dos modelos Pair-Cópula, que têm sido de fundamental importância para estender o conceito de dependência do caso bivariado para o caso multivariado. A metodologia de Pair-Cópula propõe a utilização de diagramas vine para a organização dos possíveis modelos. A ênfase é dada para o diagrama D-vine, que permite diversas permutações entre as séries. Por meio de simulação, é verificado o impacto dessas diferentes permutações do diagrama D-vine, e também do uso de diferentes funções de cópulas sob o cálculo do Valor em Risco (VaR). São realizadas comparações com cópulas multivariadas arquimedianas, normal e t-Student multivariadas. é apresentada uma aplicação de cópulas tetravariadas a dados reais de retornos financeiros / Abstract: The construction of multivariate distributions with asymmetric dependencies, especially with complex dependencies in the tails, is a necessary requirement in many applications, particularly in finance. The theory of copulas can be very useful in this task. In this sense, some of the proposals suggested in the literature are the Archimedean hierarchical models, Pair-Copula models and asymmetric t-Student copula. This dissertation is focused on the study and application of models of more than three dimensions through the Pair-Copula models, which have been essential to extend the concept of dependence of bivariate case to the multivariate case. The Pair-Copula methodology proposes the use of vine tree for the organization the possible models. Emphasis is given to the D-vine tree, which allows permutation among the variables. The influence and the importance of the order of the variables in the D-vine in the estimation of the Value at Risk (VaR) is investigated by simulation. The pair-copula model is compared with the t-Student multivariate distribution, the multivariate Archimedean copula, and paircopula models using different copula functions. The model is also applied to estimate the VaR of a portfolio with four assets / Mestrado / Estatistica / Mestre em Estatística

This thesis is a pilot study on the subsampling methods for robust estimation in regression models when there are possible outliers in the data. Two basic proposals of the subsampling method are investigated. The main idea is to identify good data points through fitting the model to randomly chosen subsamples. Subsamples containing no outliers are identified by good fit and they are combined to form a subset of good data points. Once the combined sets containing only good data points are identified, classical estimation methods such as the least-squares method and the maximum likelihood method can be applied to do regression analysis using the combined set. Numerical evidence suggest that the subsampling method is robust against outliers with high breakdown point, and it is competitive to other robust methods in terms of both robustness and efficiency. It has wide application to a variety of regression models including the linear regression models, the non-linear regression models and the generalized linear regression models. Research is ongoing with the aim of making this method an effective and practical method for robust inference on regression models.