Recentes avanços tecnológicos e computacionais trouxeram alternativas que acarretaram em mudanças na forma com que se faz análises e visualizações de dados. Uma dessas mudanças caracteriza-se no uso de plataformas interativas e gráficos dinâmicos para a realização de tais análises. Desta maneira, análises e visualizações de dados não se limitam mais a um ambiente estático, de modo que, explorar a interatividade pode possibilitar um maior leque na investigação e apresentação dos dados. O presente trabalho tem como objetivo propor um aplicativo interativo, de fácil uso e interface amigável, que viabilize estudos, análises descritivas e ajustes de modelos lineares generalizados. Este aplicativo é feito utilizando o pacote shiny no ambiente R de computação estatística com a proposta de atuar como ferramenta de apoio para a pesquisa e ensino da estatística. Usuários sem afinidade em programação podem explorar os dados e realizar o ajuste de modelos lineares generalizados sem digitar uma linha código. Em relação ao ensino, a dinâmica e interatividade do aplicativo proporcionam ao aluno uma investigação descomplicada de métodos envolvidos, tornando mais fácil a assimilação de conceitos relacionados ao tema. / Recent technological and computational advances have brought alternatives that have led to changes in the way data analyzes and visualizations are done. One of these changes is characterized by the use of interactive platforms and dynamic graphics to carry out such analyzes. In this way, data analyzes and visualizations are no longer limited to a static environment, so exploring this dynamic interactivity can enable a wider range of data exploration and presentation. The present work aims to propose an interactive application, easy to use and with user-friendly interface, which enables studies and descriptive analysis and fit generalized linear models. This application is made using the shiny package in the R environment of statistical computing. The purpose of the application is to act as a support tool for statistical research and teaching. Users with no familiarity in programming can explore the data and perform the fit of generalized linear models without typing a single code line. Regarding teaching, the dynamics and interactivity of the application gives the student an uncomplicated way to investigate the methods involved, making it easier to assimilate concepts related to the subject.

Housing prices are of crucial importance in financial stability management. The severe financial crises that originated in the housing market in the US and subsequently spread throughout the world highlighted the crucial role that the housing market plays in preserving financial stability. After the severe housing market crash, many financial institutions in the US suffered from high default rates, severe liquidity shortages, and even bankruptcy. Against this background, researchers have sought to use econometric models to capture and forecast prices of homes. Available empirical research indicates that nonlinear models may be suitable for modelling price cycles. Accordingly, this thesis focuses primarily on using nonlinear models to empirically investigate cyclical patterns in housing prices. More specifically, the content of this thesis can be summarised in three essays which complement the existing literature on price modelling by using nonlinear models. The first essay contributes to the literature by testing the ability of regime switching models to capture and forecast house prices. The second essay examines the impact of banking factors on house price fluctuations. To account for house price characteristics, the regime switching model and generalised autoregressive conditionally heteroscedastic (GARCH) in-mean model have been used. The final essay investigates the effect of structural breaks on the unit root test and shows that a time-varying GARCH in-mean model can be used to estimate the housing price cycle in the UK.

A análise de dados binários é usualmente feita através da regressão logística, mas esse modelo possui limitações. Modificar a função de ligação da regressão permite maior flexibilidade na modelagem e diversas propostas já foram feitas nessa área. No entanto, não se sabe de nenhum pacote estatístico capaz de estimar esses modelos, o que dificulta sua utilização. O presente trabalho propõe uma implementação em R de quatro modelos de regressão binária com função de ligação paramétrica usando tanto a abordagem frequentista como a Bayesiana. / Binary data analysis is usually conducted with logistic regression, but this model has limitations. Modifying the link function allows greater flexibility in modelling and several proposals have been made on the field. However, to date there are no packages capable of estimating these models imposing some difficulties to utilize them. The present work develops an R implementation of four binary regression models with parametric link functions in both frequentist and Bayesian approaches.

High frequency time series data have become increasingly common. In many settings, such as the medical sciences or economics, these series may additionally display semi-reflective boundaries. These are boundaries, either physically existing, arbitrarily set, or determined based on inherent qualities of the series, which may be exceeded and yet based on probable consequences offer incentives to return to mid-range levels. In a lane control setting, Dawson, Cavanaugh, Zamba, and Rizzo (2010) have previously developed a weighted third-order autoregressive model utilizing flat, linear, and quadratic projections with a signed error term in order to depict key features of driving behavior, where the probability of a negative residual is predicted via logistic regression. In this driving application, the intercept (Λ0) of the logistic regression model describes the central tendency of a particular driver while the slope parameter (Λ1 ) can be intuitively defined as a representation of the propensity of the series to return to mid-range levels. We call this therefore the "re-centering" parameter, though this is a slight misnomer since the logistic model does not describe the position of the series, but rather the probability of a negative residual. In this framework a multi-step estimation algorithm, which we label as the Single-Pass method, was provided. In addition to investigating the statistical properties of the Single-Pass method, several other estimation techniques are investigated. These techniques include an Iterated Grid Search, which utilizes the underlying likelihood model, and four modified versions of the Single-Pass method. These Modified Single-Pass (MSP) techniques utilize respectively unconstrained least squares estimation for the vector of projection coefficients (Β), use unconstrained linear regression with a post-hoc application of the summation constraint, reduce the regression model to include only the flat and linear projections, or implement the Least Absolute Shrinkage and Selection Operator (LASSO). For each of these techniques, mean bias, confidence intervals, and coverage probabilities were calculated which indicated that of the modifications only the first two were promising alternatives. In a driving application, we therefore considered these two modified techniques along with the Single-Pass and Iterative Grid Search. It was found that though each of these methods remains biased with generally lower than ideal coverage probabilities, in a lane control setting they are each able to distinguish between two populations based on disease status. It has also been found that the re-centering parameter, estimated based on data collected in a driving simulator amongst a control population, is significantly correlated with neuropsychological outcomes as well as driving errors performed on-road. Several of these correlations were apparent regardless of the estimation technique, indicating real-world validity of the model across related assessments. Additionally, the Iterated Grid Search produces estimates that are most distinct with generally lower bias and improved coverage with the exception of the estimate of Λ1. However this method also requires potentially large time and memory commitments as compared to the other techniques considered. Thus the optimal estimation scheme is dependent upon the situation. When feasible the Iterated Grid Search appears to be the best overall method currently available. However if time or memory is a limiting factor, or if a reliable estimate of the re-centering parameter with reasonably accurate estimation of the Β vector is desired, the Modified Single-Pass technique utilizing unconstrained linear regression followed by implementation of the summation constraint is a sensible alternative.

Abstract not available

<p>Saab Ericsson Space AB develops products for space for a predetermined price. Since the price is fixed, it is crucial to have a reliable prediction model to estimate the effort needed to develop the product. In general software effort estimation is difficult, and at the software department this is a problem.</p><p>By analyzing metrics, collected from former projects, different prediction models are developed to estimate the number of person hours a software project will require. Models for predicting the effort before a project begins is first developed. Only a few variables are known at this state of a project. The models developed are compared to a current model used at the company. Linear regression models improve the estimate error with nine percent units and nonlinear regression models improve the result even more. The model used today is also calibrated to improve its predictions. A principal component regression model is developed as well. Also a model to improve the estimate during an ongoing project is developed. This is a new approach, and comparison with the first estimate is the only evaluation.</p><p>The result is an improved prediction model. There are several models that perform better than the one used today. In the discussion, positive and negative aspects of the models are debated, leading to the choice of a model, recommended for future use.</p>

<p>Linear time-invariant approximations of nonlinear systems are used in many applications and can be obtained in several ways. For example, using system identification and the prediction-error method, it is always possible to estimate a linear model without considering the fact that the input and output measurements in many cases come from a nonlinear system. One of the main objectives of this thesis is to explain some properties of such approximate models.</p><p>More specifically, linear time-invariant models that are optimal approximations in the sense that they minimize a mean-square error criterion are considered. Linear models, both with and without a noise description, are studied. Some interesting, but in applications usually undesirable, properties of such optimal models are pointed out. It is shown that the optimal linear model can be very sensitive to small nonlinearities. Hence, the linear approximation of an almost linear system can be useless for some applications, such as robust control design. Furthermore, it is shown that standard validation methods, designed for identification of linear systems, cannot always be used to validate an optimal linear approximation of a nonlinear system.</p><p>In order to improve the models, conditions on the input signal that imply various useful properties of the linear approximations are given. It is shown, for instance, that minimum phase filtered white noise in many senses is a good choice of input signal. Furthermore, the class of separable signals is studied in detail. This class contains Gaussian signals and it turns out that these signals are especially useful for obtaining approximations of generalized Wiener-Hammerstein systems. It is also shown that some random multisine signals are separable. In addition, some theoretical results about almost linear systems are presented.</p><p>In standard methods for robust control design, the size of the model error is assumed to be known for all input signals. However, in many situations, this is not a realistic assumption when a nonlinear system is approximated with a linear model. In this thesis, it is described how robust control design of some nonlinear systems can be performed based on a discrete-time linear model and a model error model valid only for bounded inputs.</p><p>It is sometimes undesirable that small nonlinearities in a system influence the linear approximation of it. In some cases, this influence can be reduced if a small nonlinearity is included in the model. In this thesis, an identification method with this option is presented for nonlinear autoregressive systems with external inputs. Using this method, models with a parametric linear part and a nonparametric Lipschitz continuous nonlinear part can be estimated by solving a convex optimization problem.</p> / <p>Linjära tidsinvarianta approximationer av olinjära system har många användningsområden och kan tas fram på flera sätt. Om man har mätningar av in- och utsignalerna från ett olinjärt system kan man till exempel använda systemidentifiering och prediktionsfelsmetoden för att skatta en linjär modell utan att ta hänsyn till att systemet egentligen är olinjärt. Ett av huvudmålen med den här avhandlingen är att beskriva egenskaper för sådana approximativa modeller.</p><p>Framförallt studeras linjära tidsinvarianta modeller som är optimala approximationer i meningen att de minimerar ett kriterium baserat på medelkvadratfelet. Brusmodeller kan inkluderas i dessa modelltyper och både fallet med och utan brusmodell studeras här. Modeller som är optimala i medelkvadratfelsmening visar sig kunna uppvisa ett antal intressanta, men ibland oönskade, egenskaper. Bland annat visas det att en optimal linjär modell kan vara mycket känslig för små olinjäriteter. Denna känslighet är inte önskvärd i de flesta tillämpningar och innebär att en linjär approximation av ett nästan linjärt system kan vara oanvändbar för till exempel robust reglerdesign. Vidare visas det att en del valideringsmetoder som är framtagna för linjära system inte alltid kan användas för validering av linjära approximationer av olinjära system.</p><p>Man kan dock göra de optimala linjära modellerna mer användbara genom att välja lämpliga insignaler. Bland annat visas det att minfasfiltrerat vitt brus i många avseenden är ett bra val av insignal. Klassen av separabla signaler detaljstuderas också. Denna klass innehåller till exempel alla gaussiska signaler och just dessa signaler visar sig vara speciellt användbara för att ta fram approximationer av generaliserade wiener-hammerstein-system. Dessutom visas det att en viss typ av slumpmässiga multisinussignaler är separabel. Några teoretiska resultat om nästan linjära system presenteras också.</p><p>De flesta metoder för robust reglerdesign kan bara användas om storleken på modellfelet är känd för alla tänkbara insignaler. Detta är emellertid ofta inte realistiskt när ett olinjärt system approximeras med en linjär modell. I denna avhandling beskrivs därför ett alternativt sätt att göra en robust reglerdesign baserat på en tidsdiskret modell och en modellfelsmodell som bara är giltig för begränsade insignaler.</p><p>Ibland skulle det vara önskvärt om en linjär modell av ett system inte påverkades av förekomsten av små olinjäriteter i systemet. Denna oönskade påverkan kan i vissa fall reduceras om en liten olinjär term tas med i modellen. En identifieringsmetod för olinjära autoregressiva system med externa insignaler där denna möjlighet finns beskrivs här. Med hjälp av denna metod kan modeller som består av en parametrisk linjär del och en ickeparametrisk lipschitzkontinuerlig olinjär del skattas genom att man löser ett konvext optimeringsproblem.</p>

A trajectory piecewise-linear (TPWL) approach is developed for a computational fluid dynamics (CFD) model of the two-dimensional Euler equations. The approach uses a weighted combination of linearized models to represent the nonlinear CFD system. The proper orthogonal decomposition (POD) is then used to create a reduced-space basis, onto which the TPWL model is projected. This projection yields an efficient reduced-order model of the nonlinear system, which does not require the evaluation of any full-order system residuals. The method is applied to the case of flow through an actively controlled supersonic diffuser. With an appropriate choice of linearization points and POD basis vectors, the method is found to yield accurate results, including cases with significant shock motion. / Singapore-MIT Alliance (SMA)

Linear time-invariant approximations of nonlinear systems are used in many applications and can be obtained in several ways. For example, using system identification and the prediction-error method, it is always possible to estimate a linear model without considering the fact that the input and output measurements in many cases come from a nonlinear system. One of the main objectives of this thesis is to explain some properties of such approximate models. More specifically, linear time-invariant models that are optimal approximations in the sense that they minimize a mean-square error criterion are considered. Linear models, both with and without a noise description, are studied. Some interesting, but in applications usually undesirable, properties of such optimal models are pointed out. It is shown that the optimal linear model can be very sensitive to small nonlinearities. Hence, the linear approximation of an almost linear system can be useless for some applications, such as robust control design. Furthermore, it is shown that standard validation methods, designed for identification of linear systems, cannot always be used to validate an optimal linear approximation of a nonlinear system. In order to improve the models, conditions on the input signal that imply various useful properties of the linear approximations are given. It is shown, for instance, that minimum phase filtered white noise in many senses is a good choice of input signal. Furthermore, the class of separable signals is studied in detail. This class contains Gaussian signals and it turns out that these signals are especially useful for obtaining approximations of generalized Wiener-Hammerstein systems. It is also shown that some random multisine signals are separable. In addition, some theoretical results about almost linear systems are presented. In standard methods for robust control design, the size of the model error is assumed to be known for all input signals. However, in many situations, this is not a realistic assumption when a nonlinear system is approximated with a linear model. In this thesis, it is described how robust control design of some nonlinear systems can be performed based on a discrete-time linear model and a model error model valid only for bounded inputs. It is sometimes undesirable that small nonlinearities in a system influence the linear approximation of it. In some cases, this influence can be reduced if a small nonlinearity is included in the model. In this thesis, an identification method with this option is presented for nonlinear autoregressive systems with external inputs. Using this method, models with a parametric linear part and a nonparametric Lipschitz continuous nonlinear part can be estimated by solving a convex optimization problem. / Linjära tidsinvarianta approximationer av olinjära system har många användningsområden och kan tas fram på flera sätt. Om man har mätningar av in- och utsignalerna från ett olinjärt system kan man till exempel använda systemidentifiering och prediktionsfelsmetoden för att skatta en linjär modell utan att ta hänsyn till att systemet egentligen är olinjärt. Ett av huvudmålen med den här avhandlingen är att beskriva egenskaper för sådana approximativa modeller. Framförallt studeras linjära tidsinvarianta modeller som är optimala approximationer i meningen att de minimerar ett kriterium baserat på medelkvadratfelet. Brusmodeller kan inkluderas i dessa modelltyper och både fallet med och utan brusmodell studeras här. Modeller som är optimala i medelkvadratfelsmening visar sig kunna uppvisa ett antal intressanta, men ibland oönskade, egenskaper. Bland annat visas det att en optimal linjär modell kan vara mycket känslig för små olinjäriteter. Denna känslighet är inte önskvärd i de flesta tillämpningar och innebär att en linjär approximation av ett nästan linjärt system kan vara oanvändbar för till exempel robust reglerdesign. Vidare visas det att en del valideringsmetoder som är framtagna för linjära system inte alltid kan användas för validering av linjära approximationer av olinjära system. Man kan dock göra de optimala linjära modellerna mer användbara genom att välja lämpliga insignaler. Bland annat visas det att minfasfiltrerat vitt brus i många avseenden är ett bra val av insignal. Klassen av separabla signaler detaljstuderas också. Denna klass innehåller till exempel alla gaussiska signaler och just dessa signaler visar sig vara speciellt användbara för att ta fram approximationer av generaliserade wiener-hammerstein-system. Dessutom visas det att en viss typ av slumpmässiga multisinussignaler är separabel. Några teoretiska resultat om nästan linjära system presenteras också. De flesta metoder för robust reglerdesign kan bara användas om storleken på modellfelet är känd för alla tänkbara insignaler. Detta är emellertid ofta inte realistiskt när ett olinjärt system approximeras med en linjär modell. I denna avhandling beskrivs därför ett alternativt sätt att göra en robust reglerdesign baserat på en tidsdiskret modell och en modellfelsmodell som bara är giltig för begränsade insignaler. Ibland skulle det vara önskvärt om en linjär modell av ett system inte påverkades av förekomsten av små olinjäriteter i systemet. Denna oönskade påverkan kan i vissa fall reduceras om en liten olinjär term tas med i modellen. En identifieringsmetod för olinjära autoregressiva system med externa insignaler där denna möjlighet finns beskrivs här. Med hjälp av denna metod kan modeller som består av en parametrisk linjär del och en ickeparametrisk lipschitzkontinuerlig olinjär del skattas genom att man löser ett konvext optimeringsproblem.

After the 1999 Marmara Earthquake, social, economic and engineering studies on earthquakes became more intensive. The Turkish Catastrophe Insurance Pool (TCIP) was established after the Marmara Earthquake to share the deficit in the budget of the Government. The TCIP has become a data source for researchers, consisting of variables such as number of claims, claim amount and magnitude. In this thesis, the TCIP earthquake claims, collected between 2000 and 2008, are studied. The number of claims and claim payments (aggregate claim amount) are modeled by using Generalized Linear Models (GLM). Observed sudden jumps in claim data are represented by using the exponential kernel function. Model parameters are estimated by using the Maximum Likelihood Estimation (MLE). The results can be used as recommendation in the computation of expected value of the aggregate claim amounts and the premiums of the TCIP.