Mainz, Universiẗat, Diss., 2001.

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Submitted by GABRIEL DIAZ ITURRY null (gabriel.diaz.iturry@gmail.com) on 2017-05-04T14:59:10Z No. of bitstreams: 1 dissertacao_GDI.pdf: 7646479 bytes, checksum: 41982d1bb134afa5cd32f6db91fda5e9 (MD5) / Approved for entry into archive by Luiz Galeffi (luizgaleffi@gmail.com) on 2017-05-05T14:41:22Z (GMT) No. of bitstreams: 1 diaziturry_g_me_rcla.pdf: 7646479 bytes, checksum: 41982d1bb134afa5cd32f6db91fda5e9 (MD5) / Made available in DSpace on 2017-05-05T14:41:22Z (GMT). No. of bitstreams: 1 diaziturry_g_me_rcla.pdf: 7646479 bytes, checksum: 41982d1bb134afa5cd32f6db91fda5e9 (MD5) Previous issue date: 2017-02-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / 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. / 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.

Submitted by Alice Araujo (alice.caraujo@ufpe.br) on 2018-05-10T18:25:09Z No. of bitstreams: 1 TESE Ana Hermínia Andrade e Silva.pdf: 1090771 bytes, checksum: 8e2a4ceb20b4376bc5081da0e2216081 (MD5) / Made available in DSpace on 2018-05-10T18:25:09Z (GMT). No. of bitstreams: 1 TESE Ana Hermínia Andrade e Silva.pdf: 1090771 bytes, checksum: 8e2a4ceb20b4376bc5081da0e2216081 (MD5) Previous issue date: 2017-02-14 / CAPES / Na presente tese de doutorado, apresentamos estimadores dos parâmetros que indexam as transformações de Manly e Box-Cox, usadas para transformar a variável resposta do modelo de regressão linear, e também testes de hipóteses. A tese é composta por quatro capítulos. No Capítulo 2, desenvolvemos dois testes escore para a transformação de Box-Cox e dois testes escore para a transformação de Manly (Ts e Ts0), para estimar os parâmetros das transformações. A principal desvantagem da transformação de Box-Cox é que ela só pode ser aplicada a dados não negativos. Por outro lado, a transformação de Manly pode ser aplicada a qualquer dado real. Utilizamos simulações de Monte Carlo para avaliarmos os desempenhos dos estimadores e testes propostos. O principal resultado é que o teste Ts teve melhor desempenho que o teste Ts0, tanto em tamanho quanto em poder. No Capítulo 3 apresentamos refinamentos para os testes escore desenvolvidos no Capítulo 2 usando o fast double bootstrap. Seu desempenho foi avaliado via simulações de Monte Carlo. O resultado principal é que o teste fast double bootstrap é superior ao teste bootstrap clássico. No Capítulo 4 propusemos sete estimadores não-paramétricos para estimar os parâmetros que indexam as transformações de Box-Cox e Manly, com base em testes de normalidade. Realizamos simulações de Monte Carlo em três casos. Comparamos os desempenhos dos estimadores não-paramétricos com o do estimador de máxima verosimilhança (EMV). No terceiro caso, pelo menos um estimador não-paramétrico apresenta desempenho superior ao EMV. / In this PhD dissertation we develop estimators and tests on the parameters that index the Manly and Box-Cox transformations, which are used to transform the response variable of the linear regression model. It is composed of four chapters. In Chapter 2 we develop two score tests for the Box-Cox and Manly transformations (Ts and Ts0). The main disadvantage of the Box-Cox transformation is that it can only be applied to positive data. In contrast, Manly transformation can be applied to any real data. We performed Monte Carlo simulations to evaluate the finite sample performances of the pro-posed estimators and tests. The results show that the Ts test outperforms Ts0 test, both in size and in power. In Chapter 3, we present refinements for the score tests developed in Chapter 2 using the fast double bootstrap. We performed Monte Carlo simulations to evaluate the effectiveness of such a bootstrap scheme. The main result is that the fast double bootstrap is superior to the standard bootstrap. In Chapter 4, we propose seven nonparametric estimators for the parameters that index the Box-Cox and Manly transformations, based on normality tests. We performed Monte Carlo simulations in three cases. We compare performances of the nonparametric estimators with that of the maximum likelihood estimator (MLE).

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In recent years, the sequential Monte Carlo method, also referred to as the particle filter has emerged as a powerful methodology for solving the generally difficult nonlinear, non-Gaussian optimal filtering problem. The underlying idea is to use a randomly weighted set of samples to recursively build in time, a point-mass approximation of the true posterior PDF. With this approximation, one can recursively estimate typically intractable posterior expectations of interest. Indeed, the PF can be applied to a very large class of models. Within the last few years, the aforementioned advantages have propelled research on particle filtering and its applications. The subject of this thesis is to the extend the theories and applications of the particle filter. The main contributions of this thesis are described as follows: 1. We consider the optimal filtering problem for a class of partially observed non-Gaussian dynamic state space models. In this class, the process equation consists of a combination of linear and nonlinear states, and the process noise for the nonlinear state update is a mixture of Gaussians. In order to solve this problem, we propose a novel method based on an efficient combination of the approximate conditional mean filter and the sequential importance sampling particle filter. 2. We address the problem of channel equalization and phase noise suppression in orthogonal frequency division multiplexing (OFDM) systems. For OFDM systems, random phase noise introduced by the local oscillator causes two effects: the common phase error (CPE), and the intercarrier interference (ICI). The performance of coherent OFDM systems greatly depends on the ability to accurately estimate the effective dynamic channel i.e., the combined effect of the CPE and the time-varying frequency selective channel. With this in mind, we propose an algorithm that equalizes in the frequency domain, and uses a pilot tone aided particle filter to track/estimate the effective dynamic channel in the time domain. To increase efficiency, we implement the particle filter via a combination of sequential importance sampling, Rao-Blackwellization, and strategies stemming from the auxiliary particle filter. / Thesis / Master of Applied Science (MASc)