In recent years additional requirements have been imposed on financial institutions, including Central Counterparty clearing houses (CCPs), as an attempt to assess quantitative measures of their exposure to different types of risk. One of these requirements results in a need to perform stress tests to check the resilience in case of a stressed market/crisis. However, financial markets develop over time and this leads to a situation where some instruments traded today are not present at the chosen date because they were introduced after the considered historical event. Based on current routines, the main goal of this thesis is to provide a more sophisticated method to impute (fill in) historical missing data as a preparatory work in the context of stress testing. The models considered in this paper include two methods currently regarded as state-of-the-art techniques, based on maximum likelihood estimation (MLE) and multiple imputation (MI), together with a third alternative approach involving copulas. The different methods are applied on historical return data of commodity futures contracts from the Nordic energy market. By using conventional error metrics, and out-of-sample log-likelihood, the conclusion is that it is very hard (in general) to distinguish the performance of each method, or draw any conclusion about how good the models are in comparison to each other. Even if the Student’s t-distribution seems (in general) to be a more adequate assumption regarding the data compared to the normal distribution, all the models are showing quite poor performance. However, by analysing the conditional distributions more thoroughly, and evaluating how well each model performs by extracting certain quantile values, the performance of each method is increased significantly. By comparing the different models (when imputing more extreme quantile values) it can be concluded that all methods produce satisfying results, even if the g-copula and t-copula models seems to be more robust than the respective linear models. / På senare år har ytterligare krav införts för finansiella institut (t.ex. Clearinghus) i ett försök att fastställa kvantitativa mått på deras exponering mot olika typer av risker. Ett av dessa krav innebär att utföra stresstester för att uppskatta motståndskraften under stressade marknader/kriser. Dock förändras finansiella marknader över tiden vilket leder till att vissa instrument som handlas idag inte fanns under den dåvarande perioden, eftersom de introducerades vid ett senare tillfälle. Baserat på nuvarande rutiner så är målet med detta arbete att tillhandahålla en mer sofistikerad metod för imputation (ifyllnad) av historisk data som ett förberedande arbete i utförandet av stresstester. I denna rapport implementeras två modeller som betraktas som de bäst presterande metoderna idag, baserade på maximum likelihood estimering (MLE) och multiple imputation (MI), samt en tredje alternativ metod som involverar copulas. Modellerna tillämpas på historisk data förterminskontrakt från den nordiska energimarkanden. Genom att använda väl etablerade mätmetoder för att skatta noggrannheten förrespektive modell, är det väldigt svårt (generellt) att särskilja prestandan för varje metod, eller att dra några slutsatser om hur bra varje modell är i jämförelse med varandra. även om Students t-fördelningen verkar (generellt) vara ett mer adekvat antagande rörande datan i jämförelse med normalfördelningen, så visar alla modeller ganska svag prestanda vid en första anblick. Däremot, genom att undersöka de betingade fördelningarna mer noggrant, för att se hur väl varje modell presterar genom att extrahera specifika kvantilvärden, kan varje metod förbättras markant. Genom att jämföra de olika modellerna (vid imputering av mer extrema kvantilvärden) kan slutsatsen dras att alla metoder producerar tillfredställande resultat, även om g-copula och t-copula modellerna verkar vara mer robusta än de motsvarande linjära modellerna.

Este texto apresenta um método alternativo de regressão que é denominado regressão L1. Este método é robusto com relação a outliers na variável Y enquanto o método tradicional, mínimos quadrados, não oferece robustez a este tipo de outlier. Neste trabalho reanalisaremos os dados sobre imóveis apresentados por Narula e Wellington (1977) à luz da regressão L1. Ilustraremos os principais resultados inferenciais como: interpretação do modelo, construção de intervalos de confiança e testes de hipóteses para os parâmetros, análise de medidas de qualidade do ajuste do modelo e também utilizaremos medidas de diagnóstico para destacar observações influentes. Dentre as medidas de influência utilizaremos a diferença de verossimilhanças e a diferença de verossimilhanças condicional. / This text presents an alternative method of regression that is called L1 regression. This method is robust to outliers in the Y variable while the traditional least squares method does not provide robustness to this type of outlier. In this work we will review the data about houses presented by Narula and Wellington (1977) in the light of the L1 regression. We will illustrate the main inferential results such as: model interpretation, construction of confidence intervals and hypothesis tests for the parameters, analysis of quality measures of model fit and also use diagnostic measures to highlight influential observations. Among the measures of influence we will use the likelihood displacement and the conditional likelihood displacement.

This Thesis deals with the methods for detection of the outliers and influential points based on method of least squares. The first part of the thesis summarizes the teoretical findings of the method of least squares and both methods for detection of the outliers and influential points based on the method of least squares and also based on robust regression. The practical part of this thesis deals with the application of classic methods for detection of the outliers and influential points on three types of datasets (artifical data, data from specialized literature and real data). The results of the application are subject to qualitative comparisson with the results produced by the methods for detection of the outliers and influentials point based on the robust regression.

Profile monitoring is a relatively new approach in quality control best used where the process data follow a profile (or curve) at each time period. The essential idea for profile monitoring is to model the profile via some parametric, nonparametric, and semiparametric methods and then monitor the fitted profiles or the estimated random effects over time to determine if there have been changes in the profiles. The majority of previous studies in profile monitoring focused on the parametric modeling of either linear or nonlinear profiles, with both fixed and random effects, under the assumption of correct model specification. Our work considers those cases where the parametric model for the family of profiles is unknown or at least uncertain. Consequently, we consider monitoring profiles via two techniques, a nonparametric technique and a semiparametric procedure that combines both parametric and nonparametric profile fits, a procedure we refer to as model robust profile monitoring (MRPM). Also, we incorporate a mixed model approach to both the parametric and nonparametric model fits. For the mixed effects models, the MMRPM method is an extension of the MRPM method which incorporates a mixed model approach to both parametric and nonparametric model fits to account for the correlation within profiles and to deal with the collection of profiles as a random sample from a common population. For each case, we formulated two Hotelling's T 2 statistics, one based on the estimated random effects and one based on the fitted values, and obtained the corresponding control limits. In addition,we used two different formulas for the estimated variancecovariance matrix: one based on the pooled sample variance-covariance matrix estimator and a second one based on the estimated variance-covariance matrix based on successive differences. A Monte Carlo study was performed to compare the integrated mean square errors (IMSE) and the probability of signal of the parametric, nonparametric, and semiparametric approaches. Both correlated and uncorrelated errors structure scenarios were evaluated for varying amounts of model misspecification, number of profiles, number of observations per profile, shift location, and in- and out-of-control situations. The semiparametric (MMRPM) method for uncorrelated and correlated scenarios was competitive and, often, clearly superior with the parametric and nonparametric over all levels of misspecification. For a correctly specified model, the IMSE and the simulated probability of signal for the parametric and theMMRPM methods were identical (or nearly so). For the severe modelmisspecification case, the nonparametric andMMRPM methods were identical (or nearly so). For the mild model misspecification case, the MMRPM method was superior to the parametric and nonparametric methods. Therefore, this simulation supports the claim that the MMRPM method is robust to model misspecification. In addition, the MMRPM method performed better for data sets with correlated error structure. Also, the performances of the nonparametric and MMRPM methods improved as the number of observations per profile increases since more observations over the same range of X generally enables more knots to be used by the penalized spline method, resulting in greater flexibility and improved fits in the nonparametric curves and consequently, the semiparametric curves. The parametric, nonparametric and semiparametric approaches were utilized for fitting the relationship between torque produced by an engine and engine speed in the automotive industry. Then, we used a Hotelling's T 2 statistic based on the estimated random effects to conduct Phase I studies to determine the outlying profiles. The parametric, nonparametric and seminonparametric methods showed that the process was stable. Despite the fact that all three methods reach the same conclusion regarding the –in-control– status of each profile, the nonparametric and MMRPM results provide a better description of the actual behavior of each profile. Thus, the nonparametric and MMRPM methods give the user greater ability to properly interpret the true relationship between engine speed and torque for this type of engine and an increased likelihood of detecting unusual engines in future production. Finally, we conclude that the nonparametric and semiparametric approaches performed better than the parametric approach when the user's model is misspecified. The case study demonstrates that, the proposed nonparametric and semiparametric methods are shown to be more efficient, flexible and robust to model misspecification for Phase I profile monitoring in a practical application. Thus, our methods are robust to the common problem of model misspecification. We also found that both the nonparametric and the semiparametric methods result in charts with good abilities to detect changes in Phase I data, and in charts with easily calculated control limits. The proposed methods provide greater flexibility and efficiency than current parametric methods used in profile monitoring for Phase I that rely on correct model specification, an unrealistic situation in many practical problems in industrial applications. / Ph. D.

L'architecture modulaire est une caractéristique distinctive des circuits cérébraux. En particulier, il a été observé l'existence de connexions réciproques entre des zones fonctionnellement interconnectées dans le cortex, et qui par ailleurs sont hiérarchiquement organisées. De plus, le développement évolutif est une autre caractéristique distinctive des espèces vivantes ; même les virus sont capables d'adaptation pour mieux répondre à de nouvelles conditions environnementales. En tenant compte de ces deux importants aspects, nous avons construit un nouvel et unique outil de simulation permettant de modéliser et d'étudier l'évolution des circuits multi-modulaires hiérarchiques. Dans ce modèle, chaque module est représenté par des réseaux de neurones impulsionels et caractérisé à la fois par des changements d'activités neurales imbriquées et par la plasticité synaptique. La morte cellulaire, la plasticité synaptique et l'apoptose intégrés dans le modèle créent des liens auto-associatifs au sein des modules. Ces liens peuvent générer une activité zonale qui reflète l'évolution de la connectivité fonctionnelle à l'intérieur comme à l'extérieur des modules, et donc entre les plusieurs modules neuronaux. L'activité bioélectrique de chaque module est enregistrée au moyen des électrodes virtuelles. Les signaux, electrochipogrammes (EChG), sont analysés par les méthodes fréquentiels et les méthodes de potentiels évoqués afin de trouver des généralités dans le comportement émergeant. En plus de ces méthodes conventionnelles, nous proposons une nouvelle approche de régression non-linéaire structurelle afin de fournir des outils plus puissants et mieux adaptés aux données habituellement analysées dans ce domaine. Nous avons donc testé l'effet d'un stimulus externe sur le développement de liens fonctionnels d'un réseau neuronaux. Le circuit est structuré hiérarchiquement avec un unique module sensoriel et d'autres modules constitués de deux voies parallèles organisées aussi de façon hiérarchique. Nos résultats montrent que les circuits modélisés manifestent un comportement similaire que les circuits biologiques réels. En particulier, tous les éléments du circuit peuvent traiter et maintenir des patterns d'activité liés à la disparition du stimulus. Les résultats obtenus dans nos expériences apportent un éclairage sur les processus émergents et coordonnés de l'activité électrique enregistrée par des EEG de circuits inter-corticaux hiérarchiques et évolutifs qui sont artificiels ou réels. Plus généralement, notre approche concernant les signaux EEG pourrait être étendue à la modélisation d'une vaste variété des processus cognitifs et comportementaux. / Modular architecture is a hallmark of many brain circuits. Particularly, in the cerebral cortex it has been observed that reciprocal connections are often present between functionally interconnected areas that are hierarchically organized. Evolutionary development is another distinctive characteristic of living species, even the simplest viruses are capable to adapt to better fit new environmental conditions. Having hierarchical architectures and evolutionary features in mind, we build unique and novel simulation framework, which allows us to model and to study evolving hierarchically organized circuits of modules of spiking neural networks. Each module is characterized by embedded neural development and expression of spike timing dependent plasticity. Cell death, synaptic plasticity and projection pruning, embedded in the neural model, drive the build-up of auto-associative links within each module, which generate an areal activity that reflect the changes in the corresponding functional connectivity within and between neuronal modules. Bio-electric activity of each module is recorded by means of virtual electrodes and these signals, called electrochipograms (EChG), are analyzed by time and frequency domain methods in order to find general patterns of emerging behavior. Beside time and frequency domain analysis methods, a novel robust non-linear structural regression approach is proposed to provide researchers with more powerful tools specially adapted to the data typically used in the domain. We tested the effect of an external stimulus at fixed frequency fed to a sensory module, which pro jecting its activity to two hierarchically organized parallel pathways. We found that modeled circuits manifest behavior similar in certain aspects to that of real brains. We show evidence that all networks of modules are able to maintain long patterns of activity associated with the stimulus offset. These findings bring new insights to the understanding of EEG-like signals, both real and virtual. The findings prove that the approach is successful and could be extended to model cognitive and behavioral processes in the brains.

This project was dedicated to the problem of improving a non-invasive blood glucose monitor being developed by the VivaScan Corporation. The company has made some progress in the non-invasive blood glucose device development and approached WPI for a statistical assistance in the improvement of their model in order to predict the glucose level more accurately. The main goal of this project was to improve the ability of the non-invasive blood glucose monitor to predict the glucose values more precisely. The goal was achieved by finding and implementing the best regression model. The methods included ordinary least squared regression, partial least squares regression, robust regression method, weighted least squares regression, local regression, and ridge regression. VivaScan calibration data for seven patients were analyzed in this project. For each of these patients, the individual regression models were built and compared based on the two factors that evaluate the model prediction ability. It was determined that partial least squares and ridge regressions are two best methods among the others that were considered in this work. Using these two methods gave better glucose prediction. The additional problem of data reduction to minimize the data collection time was also considered in this work.

A Regressão Robusta surge como uma alternativa ao ajuste por mínimos quadrados quando os erros são contaminados por pontos aberrantes ou existe alguma evidência de violação das suposições do modelo. Na regressão clássica existem critérios de seleção de modelos e medidas de diagnóstico que são muito conhecidos. O objetivo deste trabalho é apresentar os principais critérios robustos de seleção de modelos e medidas de detecção de pontos aberrantes, assim como analisar e comparar o desempenho destes de acordo com diferentes cenários para determinar quais deles se ajustam melhor a determinadas situações. Os critérios de validação cruzada usando simulações de Monte Carlo e o Critério de Informação Bayesiano são conhecidos por desenvolver-se de forma adequada na identificação de modelos. Na dissertação confirmou-se este fato e além disso, suas alternativas robustas também destacam-se neste aspecto. A análise de resíduos constitui uma forte ferramenta da análise diagnóstico de um modelo, no trabalho detectou-se que a análise clássica de resíduos sobre o ajuste do modelo de regressão linear robusta, assim como a análise das ponderações das observações, são medidas de detecção de pontos aberrantes eficientes. Foram aplicados os critérios e medidas analisados ao conjunto de dados obtido da Estação Meteorológica do Instituto de Astronomia, Geofísica e Ciências Atmosféricas da Universidade de São Paulo para detectar quais variáveis meteorológicas influem na temperatura mínima diária durante o ano completo, e ajustou-se um modelo que permite identificar os dias associados à entrada de sistemas frontais. / Robust Regression arises as an alternative to least squares method when errors are contaminated by outliers points or there are some evidence of violation of model assumptions. In classical regression there are several criteria for model selection and diagnostic measures that are well known. The objective of this work is to present the main robust criteria of model selection and outliers detection measures, as well as to analyze and compare their performance according to different stages to determine which of them fit better in certain situations. The cross-validation criteria using Monte Carlo simulations and Beyesian Information Criterion are known to be adequately developed in model identification. This fact was confirmed, and in addition, its robust alternatives also stand out in this aspect. The residual analysis is a strong tool for model diagnostic analysis, in this work it was detected that the classic residual analysis on the robust linear model regression fit, as well as the analysis of the observations weights, are efficient measures of outliers detection points. The analyzed criteria and measures were applied to the data set obtained from the Meteorological Station of the Astronomy, Geophysics and Atmospheric Sciences Institute of São Paulo University to detect which meteorological variables influence the daily minimum temperature during the whole year, and was fitted a model that allows identify the days associated with the entry of frontal systems.

[pt] Este trabalho tem como objetivo avaliar o uso da técnica Análise Condicionada da Demanda, que é uma metodologia que quebra o consumo de energia elétrica (neste trabalho do setor residencial) em suas partes por equipamento e por uso final, via Regressão Robusta em contrapartida à utilização da regressão clássica, na estimação do consumo de energia elétrica por uso final do setor residencial. Para isto foram realizadas análises via regressão linear múltipla e também análises via regressão robusta (estimadores robustos). Serão realizadas as duas análises para efeito de comparação entre o método clássico MQO - Mínimos Quadrados Ordinários, que não é o ideal, pois os dados violam os pressupostos para utilização desta técnica, e o método robusto, menos sensível a desvios de pressupostos / [en] This work has the purpose of evaluating the use of the technique Conditional Demand Analysis - CDA, which is a methodology that segregates the consumption of electric energy (on this work about the residential sector) is its parts per equipment and per final use through the Robust Regression, in counterpart of using the classic regression, in the estimation of the electric energy consumption for final use on the residential sector. For this purpose analyses will be made using the multiple linear regression and also analyses using the robust regression (robust estimators). The two analyses will be made for comparing the classic method Squared Minimums Usual - MQO, which is not the ideal one because the data violates the requirements for using this kind of method, and the robust method, less sensible to detours of the requirements.

No description available.

The work in this dissertation comprises aeroservoelastic simulation development, two modal filter design case studies and theoretical improvement of the modal filter. The modal filter is made robust to sensor bias. Studies have shown that the states estimated by the modal filter can be integrated into active structural control. The integration of modal filters into aircraft structural control systems is explored. Modal filters require distributed sensing to achieve accurate modal coordinate estimates. Distributed sensing technology has progressed to the point, where it is being tested on aircraft such as Ikhana and the upcoming X-56A. Previously, the modal filter was criticized for requiring too many sensors. It was never assessed for its potential benefits in aircraft control. Therefore it is of practical interest to reinvestigate the modal filter. The first case study shows that under conditions of sensor normality, the modal filter is a Gaussian efficient estimator in an aeroservoelastic environment. This is a fundamental experiment considering the fact that the modal filter has never been tested in the airflow. To perform this case study a linear aeroservoelastic code capable of modeling distributed sensing is developed and experimentally validated. From this code, a computational wing model is fitted with distributed sensing. A modal filtering design methodology is developed and applied. With distributed sensing and modal filtering feedback control is achieved. This is also compared and contrasted with a controller using state-of-the-art accelerometers. In addition, new methods of active shape control are introduced for warping an aeroelastic structure utilizing the modal filter and control surfaces. The next case study takes place in a realistic setting for an aircraft. Flexible aircraft bring challenges to the active control community. Increased gust loads, possibility of flutter, and off-design drag may detrimentally affect performance and safety. Aeroservoelastic tailoring, gust load alleviation (GLA) and active flutter suppression (AFS) may be required on future flexible air vehicles. It is found that modal filters can theoretically support these systems. The aircraft case study identifies additional steps required in the modal filtering design methodology. Distributed sensing, the modal filter and modal reference shape control are demonstrated on the X-56A flutter-unstable simulation model. It is shown that control of deformations at potentially millions of points on an aircraft vehicle can be achieved through control of a few modal coordinates. Finally modal filter robustness is theoretically improved and computationally verified. State-of-the-art modal filters have high bias sensitivity. In fact, this is so critical that state-of-the-art modal filters may never be certified for aircraft implementation. This is especially true within a flight critical control system. The solution to this problem is found through derivation of the robust modal filter. The filter combines good properties of concentration algorithms with robust re-descending M-estimation. A new trim criterion specific to the strain based modal sensing system is derived making the filter robust to asymmetric or leverage point outliers. Robust starts are introduced to improve convergence of the modal estimation system to the globally optimal solution in the presence of 100s of biased fiber optic sensors.