This thesis studies the Second-order Least Squares (SLS) estimation method in regression models with and without measurement error. Applications of the methodology in general quasi-likelihood and variance function models, censored models, and linear and generalized linear models are examined and strong consistency and asymptotic normality are established. To overcome the numerical difficulties of minimizing an objective function that involves multiple integrals, a simulation-based SLS estimator is used and its asymptotic properties are studied. Finite sample performances of the estimators in all of the studied models are investigated through simulation studies.

This thesis studies the Second-order Least Squares (SLS) estimation method in regression models with and without measurement error. Applications of the methodology in general quasi-likelihood and variance function models, censored models, and linear and generalized linear models are examined and strong consistency and asymptotic normality are established. To overcome the numerical difficulties of minimizing an objective function that involves multiple integrals, a simulation-based SLS estimator is used and its asymptotic properties are studied. Finite sample performances of the estimators in all of the studied models are investigated through simulation studies.

Maximum likelihood is an ubiquitous method used in the estimation of generalized linear mixed model (GLMM). However, the method entails computational difficulties and relies on the normality assumption for random effects. We propose a second-order least squares (SLS) estimator based on the first two marginal moments of the response variables. The proposed estimator is computationally feasible and requires less distributional assumptions than the maximum likelihood estimator. To overcome the numerical difficulties of minimizing an objective function that involves multiple integrals, a simulation-based SLS estimator is proposed. We show that the SLS estimators are consistent and asymptotically normally distributed under fairly general conditions in the framework of GLMM. Missing data is almost inevitable in longitudinal studies. Problems arise if the missing data mechanism is related to the response process. This thesis develops the proposed estimators to deal with response data missing at random by either adapting the inverse probability weight method or applying the multiple imputation approach. In practice, some of the covariates are not directly observed but are measured with error. It is well-known that simply substituting a proxy variable for the unobserved covariate in the model will generally lead to biased and inconsistent estimates. We propose the instrumental variable method for the consistent estimation of GLMM with covariate measurement error. The proposed approach does not need any parametric assumption on the distribution of the unknown covariates. This makes the method less restrictive than other methods that rely on either a parametric distribution of the covariates, or to estimate the distribution using some extra information. In the presence of data outliers, it is a concern that the SLS estimators may be vulnerable due to the second-order moments. We investigated the robustness property of the SLS estimators using their influence functions. We showed that the proposed estimators have a bounded influence function and a redescending property so they are robust to outliers. The finite sample performance and property of the SLS estimators are studied and compared with other popular estimators in the literature through simulation studies and real world data examples.

Submitted by joao barbosa campbell penna (joao.penna@vale.com) on 2015-02-20T19:44:37Z No. of bitstreams: 1 TESEFINAL_20022015.pdf: 1480842 bytes, checksum: 11e3f73bc5b243b7ed4a73b63fe90c59 (MD5) / Approved for entry into archive by GILSON ROCHA MIRANDA (gilson.miranda@fgv.br) on 2015-06-08T18:42:08Z (GMT) No. of bitstreams: 1 TESEFINAL_20022015.pdf: 1480842 bytes, checksum: 11e3f73bc5b243b7ed4a73b63fe90c59 (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2015-06-12T17:55:33Z (GMT) No. of bitstreams: 1 TESEFINAL_20022015.pdf: 1480842 bytes, checksum: 11e3f73bc5b243b7ed4a73b63fe90c59 (MD5) / Made available in DSpace on 2015-06-12T17:56:53Z (GMT). No. of bitstreams: 1 TESEFINAL_20022015.pdf: 1480842 bytes, checksum: 11e3f73bc5b243b7ed4a73b63fe90c59 (MD5) Previous issue date: 2014-12-20 / Medimos a validade da paridade descoberta de juros – PDJ - para o mercado brasileiro no período de janeiro de 2010 a julho de 2014. Testamos a equação clássica da PDJ usando o Método dos Mínimos Quadrados Ordinários. Após a estimação dos parâmetros, aplicamos o Teste de Wald e verificamos que a paridade descoberta de juros não foi validada. Estendemos a equação tradicional da PDJ para uma especificação alternativa que captura medidas de risco Brasil e de alteração na liquidez internacional. Especificamente, acrescentamos três variáveis de controle: duas variáveis dummy que capturam condições de liquidez externa e o índice de commoditie CRB, que captura o risco Brasil. Com a especificação alternativa, a hipótese de que os retornos das taxas de juros em Real, dolarizadas, são iguais aos retornos da taxas de juros contratadas em dólares, ambas sujeitas ao risco Brasil, não foi rejeitada. Em complemento à análise das taxas representativas do mercado brasileiro, procurou-se avaliar a predominância da PDJ nas operações de swap cambial realizadas pela Vale S.A.. Para tanto, a série de taxa de juros em dólares do mercado brasileiro foi substituída pela taxa em dólar dos swaps contratados pela Vale. Os resultados encontrados demonstram que, quando comparado ao comportamento do mercado, as taxas em dólares da VALE são mais sensíveis às variações das taxas em Reais. / We measure the validity of uncovered interest parity - UIP - for the Brazilian market from January, 2010 to July, 2014. We tested the classical equation of UIP using the ordinary least squares method. After the estimation, we apply the Wald test and we verify that the uncovered interest parity has not been validated. We extend the traditional UIP equation for an alternative specification that captures Brazil risk and changes in liquidity of the international market. Specifically, we add three control variables: two dummy variables that capture external liquidity conditions and the commodity index CRB, which captures Brazil risk. With the alternative specification, the hypothesis that the returns in interest rates in Real, dollarized, are equal to the return of interest rate contracted in dollars, both subject to Brazil risk, was not rejected. To complement the analysis using the interest rates existing in the Brazilian market, we tried to evaluate the prevalence of UIP in cross currency interest rate swaps carried out by Vale SA. The interest rate in dollar of the Brazilian market was replaced by the dollar rate of swaps contracted by Vale. The results show that, when compared to market behavior, the dollar rates of Vale SA. are more sensitive to changes in Reais interest rates.

Esta dissertação investiga numericamente a influência dos efeitos viscosos e elásticos em escoamentos de materiais viscoplásticos no interior de uma cavidade dirigida. O modelo mecânico empregado é constituído pelas equações de conservação de massa e pelo princípio da quantidade de movimento linear, para fluidos incompressíveis, acoplado à equação constitutiva. Esta equação modifica o modelo viscoelástico de Oldroyd-B de modo a acomodar que os tempos de relaxação e retardo do material, bem como sua viscosidade viscoplástica, dependam das mudanças de sua microestrutura. A aproximação numérica do modelo emprega o método multi-campos de Galerkin mínimos-quadrados em termos do tensor de tensão extra, do vetor velocidade e do campo de pressão. Os resultados objetivam a determinção do tamanho e localização das regiões aparentemente não-escoadas do material, bem como sua deformação elástica, intensidade de tensão, e a sua vorticidade no interior da cavidade. Os resultados claramente indicam que o padrão do escoamento é fortemente influenciado pela variação dos efeitos elásticos (variação do tempo de relaxação adimensional, θ0 * ), viscosos (variação do índice de power-law, n) e cinemáticos (variação da velocidade adimensional, U* , do escoamento) no interior da cavidade. / This dissertation investigated numerically the influence of viscous and elastic effects on flows of viscoplastic materials within a lid-driven cavity. The mechanical model used is made up of mass and momentum balance equations, coupled with the constitutive equation. This equation modifies the viscoelastic Oldroyd-B model to accommodate both relaxation and retardation times, and viscosity function, dependent on the microstructure changes. Numerical approximations of the model make use a three-field Galerkin least squares method in terms of the extra stress tensor, velocity vector and pressure field. Computations focus on the determination of the size and position of apparently unyielded regions as well as the elastic deformation, stress intensity, and the vorticity within of the cavity. Results clearly indicate that the flow pattern is strongly influenced by the elastic (variation of the dimensionless relaxation time, θ0 * ), viscous (variation of the power-law index, n) and kinematic (variation of the dimensionless flow velocity, U* ) effects within the cavity.

Esta dissertação investiga numericamente a influência dos efeitos viscosos e elásticos em escoamentos de materiais viscoplásticos no interior de uma cavidade dirigida. O modelo mecânico empregado é constituído pelas equações de conservação de massa e pelo princípio da quantidade de movimento linear, para fluidos incompressíveis, acoplado à equação constitutiva. Esta equação modifica o modelo viscoelástico de Oldroyd-B de modo a acomodar que os tempos de relaxação e retardo do material, bem como sua viscosidade viscoplástica, dependam das mudanças de sua microestrutura. A aproximação numérica do modelo emprega o método multi-campos de Galerkin mínimos-quadrados em termos do tensor de tensão extra, do vetor velocidade e do campo de pressão. Os resultados objetivam a determinção do tamanho e localização das regiões aparentemente não-escoadas do material, bem como sua deformação elástica, intensidade de tensão, e a sua vorticidade no interior da cavidade. Os resultados claramente indicam que o padrão do escoamento é fortemente influenciado pela variação dos efeitos elásticos (variação do tempo de relaxação adimensional, θ0 * ), viscosos (variação do índice de power-law, n) e cinemáticos (variação da velocidade adimensional, U* , do escoamento) no interior da cavidade. / This dissertation investigated numerically the influence of viscous and elastic effects on flows of viscoplastic materials within a lid-driven cavity. The mechanical model used is made up of mass and momentum balance equations, coupled with the constitutive equation. This equation modifies the viscoelastic Oldroyd-B model to accommodate both relaxation and retardation times, and viscosity function, dependent on the microstructure changes. Numerical approximations of the model make use a three-field Galerkin least squares method in terms of the extra stress tensor, velocity vector and pressure field. Computations focus on the determination of the size and position of apparently unyielded regions as well as the elastic deformation, stress intensity, and the vorticity within of the cavity. Results clearly indicate that the flow pattern is strongly influenced by the elastic (variation of the dimensionless relaxation time, θ0 * ), viscous (variation of the power-law index, n) and kinematic (variation of the dimensionless flow velocity, U* ) effects within the cavity.

Sem resumo / Sem abstract

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-22T09:43:37Z No. of bitstreams: 2 Dissertação - Renato de Assis Ribeiro - 2014.pdf: 2069468 bytes, checksum: 012e254e859b9e44e2da79eeeabb5c1e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-22T09:46:48Z (GMT) No. of bitstreams: 2 Dissertação - Renato de Assis Ribeiro - 2014.pdf: 2069468 bytes, checksum: 012e254e859b9e44e2da79eeeabb5c1e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-10-22T09:46:48Z (GMT). No. of bitstreams: 2 Dissertação - Renato de Assis Ribeiro - 2014.pdf: 2069468 bytes, checksum: 012e254e859b9e44e2da79eeeabb5c1e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-03-13 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work was developed with the objective of making a temporal analysis of some actual circumstances of the city of Iporá, using mathematical modeling, Interpolation and Curve Fitting by Least Squares Method. Theoretical contributions concerning the proposed methods are presented in order to enhance the knowledge on the subjects. The applications were performed using as examples situations in the everyday of the city of Iporá, namely deaths due to cancer, number of students in the Basic Education, growth of the vehicle eet, Gross Domestic Product (GDP), water consumption and population dynamics iporaense. After this process, it was concluded that the interpolation and the Least Squares Method they are two extremely useful means for modeling cases where it is necessary to nd the approximation functions. The temporal analysis, from these functions, enables to estimate, discuss possibilities and prospects, generating a critical review for each studied episode. Thus, the mathematics and in particular the methods discussed can be devices to alert and to educate, assisting in the decision making and political interventions. The work also shows that there is applicability of Interpolation and Curve Fitting by Least Squares Method in High School, which can be enriched by modeling of everyday problems. / Este trabalho foi desenvolvido com o objetivo de fazer uma análise temporal de algumas circunstâncias reais do município de Iporá, usando a modelagem matemática, a Interpola ção e o Ajuste de Curvas pelo Método dos Quadrados Mínimos. Aportes teóricos referentes aos métodos propostos são apresentados com a nalidade de aprimorar os conhecimentos sobre os assuntos. As aplicações foram realizadas tomando como exemplos situações presentes no cotidiano da cidade de Iporá, a saber: óbitos provocados por câncer, número de alunos no Ensino Básico, crescimento da frota de veículos, Produto Interno Bruto (PIB), consumo de água e dinâmica populacional iporaense. Após todo esse processo, concluiu-se que a Interpolação e o Ajuste de Curvas pelo Método dos Quadrados Mínimos são dois recursos extremamente úteis para a modelagem de casos, nos quais seja necessário encontrar funções de aproximação. A análise temporal, a partir dessas funções, permite fazer estimativas, discutir possibilidades e perspectivas, gerando uma avaliação crítica para cada episódio estudado. Desse modo, a matemática e em especial os métodos abordados podem ser artifícios para alertar e conscientizar, auxiliando no despertar de atitudes e políticas de intervenções. O trabalho mostra ainda que existe aplicabilidade da Interpolação e do Ajuste de Curvas pelo Método dos Quadrados Mínimos no Ensino Médio, que pode ser enriquecida pela modelagem de problemas cotidianos.

Diploma thesis deals with designing of algorithmus for automatic controller tunning for DC motors. Automatic tuning function consist of system identification and controller parametrization. Cascade control loop was chosen for its robustness and proper DC motor control. For electric system identification of DC motor was used recursive method of instrumental variables, because of noisy signal from current transducer. In the case of identification mechanical system, there were used least sqares method. According to identified parameters, current controller was parametrized by optimum module and revolution controller according symetrcal optimum.

This diploma thesis deals with calibration of hydraulic simulation models, especially with methods used for calibration and parameters that are modified during calibration. The literature review in the field of mathematical modeling, basic principles applied in hydraulic modeling and the current approach to calibration and data collection is done in theoretical part. In the practical part of the thesis, a hydraulic model of the group water supply system Horní Dunajovice is built and subsequently calibrated. The calibration is first performed manually for the normal operational status and then using a calibration software created for this purpose for a load case with high velocity.