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The implementation of a recently suggested class of structural change tests, which test for parameter instability in general parametric models, in the R language for statistical computing is described: Focus is given to the question how the conceptual tools can be translated into computational tools that reflect the properties and flexiblity of the underlying econometric metholody while being numerically reliable and easy to use. More precisely, the class of generalized M-fluctuation tests (Zeileis & Hornik, 2003) is implemented in the package strucchange providing easily extensible functions for computing empirical fluctuation processes and automatic tabulation of critical values for a functional capturing excessive fluctuations. Traditional significance tests are supplemented by graphical methods which do not only visualize the result of the testing procedure but also convey information about the nature and timing of the structural change and which component of the parametric model is affected by it. / Series: Research Report Series / Department of Statistics and Mathematics

Wireless sensor networks (WSNs) have received huge attention during the recent years due to their applications in a large number of areas such as environmental monitoring, health and traffic monitoring, surveillance and tracking, and monitoring and control of factories and home appliances. Also, the rapid developments in the micro electro-mechanical systems (MEMS) technology and circuit design lead to a faster spread and adoption of WSNs. Wireless sensor networks consist of a number of nodes featured in general with energy-limited sensors capable of collecting, processing and transmitting information across short distances. Clock synchronization plays an important role in designing, implementing, and operating wireless sensor networks, and it is essential in ensuring a meaningful information processing order for the data collected by the nodes. Because the timing message exchanges between different nodes are affected by unknown possibly time-varying network delay distributions, the estimation of clock offset parameters represents a challenge. This dissertation presents several robust estimation approaches of the clock offset parameters necessary for time synchronization of WSNs via the two-way message exchange mechanism. In this dissertation the main emphasis will be put on building clock phase offset estimators robust with respect to the unknown network delay distributions. Under the assumption that the delay characteristics of the uplink and the downlink are asymmetric, the clock offset estimation method using the bootstrap bias correction approach is derived. Also, the clock offset estimator using the robust Mestimation technique is presented assuming that one underlying delay distribution is mixed with another delay distribution. Next, although computationally complex, several novel, efficient, and robust estimators of clock offset based on the particle filtering technique are proposed to cope with the Gaussian or non-Gaussian delay characteristics of the underlying networks. One is the Gaussian mixture Kalman particle filter (GMKPF) method. Another is the composite particle filter (CPF) approach viewed as a composition between the Gaussian sum particle filter and the KF. Additionally, the CPF using bootstrap sampling is also presented. Finally, the iterative Gaussian mixture Kalman particle filter (IGMKPF) scheme, combining the GMKPF with a procedure for noise density estimation via an iterative mechanism, is proposed.

Dans le monde d’aujourd’hui, il est très fréquent de vouloir modéliser la relation entre deux ou plusieurs variables. Toutefois, plusieurs expériences sont laissées à l’abandon à cause de la présence systématique de données aberrantes. Ce mémoire portera sur les estimateurs robustes permettant de modéliser des séries de données contenant des valeurs aberrantes, nous aidant ainsi à tirer un maximum d’informations de ces expériences. Dans un premier temps, nous présenterons des estimateurs robustes qui nécessitent l’imposition d’un modèle paramétrique. Ensuite, nous traiterons de l’introduction des copules à ces estimateurs robustes. Finalement, nous présenterons des simulations tirées d’une expérience réelle qui consistait à modéliser le vrai poids d’un porc selon le poids mesuré par une balance, développée au centre de recherche et développement de Sherbrooke, dans l’optique d’améliorer les techniques d’alimentation de précision.

In modern data science, it is common that large-scale data are stored and processed parallelly across a great number of locations. For reasons including confidentiality concerns, only limited data information from each parallel center is eligible to be transferred. To solve these problems more efficiently, a group of communication-efficient methods are being actively developed. The first part of our investigation is the distributions of the distributed M-estimators that require a one-step update, combining data information collected from all parallel centers. We reveal that the number of centers plays a critical role. When it is not small compared with the total sample size, a non-negligible impact occurs to the limiting distributions, which turn out to be mixtures involving products of normal random variables. Based on our analysis, we propose a multiplier-bootstrap method for approximating the distributions of these one-step updated estimators. Our second contribution is that we propose two communication-efficient Newton-type algorithms, combining the M-estimator and the gradient collected from each data center. They are created by constructing two Fisher information estimators globally with those communication-efficient statistics. Enjoying a higher rate of convergence, this framework improves upon existing Newton-like methods. Moreover, we present two bias-adjusted one-step distributed estimators. When the square of the center-wise sample size is of a greater magnitude than the total number of centers, they are as efficient as the global M-estimator asymptotically. The advantages of our methods are illustrated by extensive theoretical and empirical evidences. / Statistics

L'objet de cette thèse est d'établir des résultats asymptotiques pour l'estimateur du quantile conditionnel par la méthode des polynômes locaux ainsi qu'à la généralisation de ces résultats pour les M-estimateurs. Nous étudions ces estimateurs et plus particulièrement leur représentation de Bahadur et leur biais. Nous donnons en outre un résultat sur les intervalles de confiance uniformes construits à partir de cette représentation pour le quantile conditionnel et ses dérivées.

Nesta tese, aborda-se o problema de classificaÃÃo de dados que estÃo contaminados com pa- drÃes atÃpicos. Tais padrÃes, genericamente chamados de outliers, sÃo onipresentes em conjunto de dados multivariados reais, porÃm sua detecÃÃo a priori (i.e antes de treinar um classificador) à uma tarefa de difÃcil realizaÃÃo. Como conseqÃÃncia, uma abordagem reativa, em que se desconfia da presenÃa de outliers somente apÃs um classificador previamente treinado apresen- tar baixo desempenho, à a mais comum. VÃrias estratÃgias podem entÃo ser levadas a cabo a fim de melhorar o desempenho do classificador, dentre elas escolher um classificador mais poderoso computacionalmente ou promover uma limpeza dos dados, eliminando aqueles pa- drÃes difÃceis de categorizar corretamente. Qualquer que seja a estratÃgia adotada, a presenÃa de outliers sempre irà requerer maior atenÃÃo e cuidado durante o projeto de um classificador de padrÃes. Tendo estas dificuldades em mente, nesta tese sÃo revisitados conceitos e tÃcni- cas provenientes da teoria de regressÃo robusta, em particular aqueles relacionados à estimaÃÃo M, adaptando-os ao projeto de classificadores de padrÃes capazes de lidar automaticamente com outliers. Esta adaptaÃÃo leva à proposiÃÃo de versÃes robustas de dois classificadores de padrÃes amplamente utilizados na literatura, a saber, o classificador linear dos mÃnimos qua- drados (least squares classifier, LSC) e a mÃquina de aprendizado extremo (extreme learning machine, ELM). AtravÃs de uma ampla gama de experimentos computacionais, usando dados sintÃticos e reais, mostra-se que as versÃes robustas dos classificadores supracitados apresentam desempenho consistentemente superior aos das versÃes originais. / This thesis addresses the problem of data classification when they are contaminated with atypical patterns. These patterns, generally called outliers, are omnipresent in real-world multi- variate data sets, but their a priori detection (i.e. before training the classifier) is a difficult task to perform. As a result, the most common approach is the reactive one, in which one suspects of the presence of outliers in the data only after a previously trained classifier has achieved a low performance. Several strategies can then be carried out to improve the performance of the classifier, such as to choose a more computationally powerful classifier and/or to remove the de- tected outliers from data, eliminating those patterns which are difficult to categorize properly. Whatever the strategy adopted, the presence of outliers will always require more attention and care during the design of a pattern classifier. Bearing these difficulties in mind, this thesis revi- sits concepts and techniques from the theory of robust regression, in particular those related to M-estimation, adapting them to the design of pattern classifiers which are able to automatically handle outliers. This adaptation leads to the proposal of robust versions of two pattern classi- fiers widely used in the literature, namely, least squares classifier (LSC) and extreme learning machine (ELM). Through a comprehensive set of computer experiments using synthetic and real-world data, it is shown that the proposed robust classifiers consistently outperform their original versions.

Errors of computational simulations in design of a high-speed civil transport (HSCT) are investigated. First, discretization error from a supersonic panel code, WINGDES, is considered. Second, convergence error from a structural optimization procedure using GENESIS is considered along with the Rosenbrock test problem. A grid converge study is performed to estimate the order of the discretization error in the lift coefficient (CL) of the HSCT calculated from WINGDES. A response surface (RS) model using several mesh sizes is applied to reduce the noise magnification problem associated with the Richardson extrapolation. The RS model is shown to be more efficient than Richardson extrapolation via careful use of design of experiments. A programming error caused inaccurate optimization results for the Rosenbrock test function, while inadequate convergence criteria of the structural optimization produced error in wing structural weight of the HSCT. The Weibull distribution is successfully fit to the optimization errors of both problems. The probabilistic model enables us to estimate average errors without performing very accurate optimization runs that can be expensive, by using differences between two sets of results with different optimization control parameters such as initial design points or convergence criteria. Optimization results with large errors, outliers, produced inaccurate RS approximations. A robust regression technique, M-estimation implemented by iteratively reweighted least squares (IRLS), is used to identify the outliers, which are then repaired by higher fidelity optimizations. The IRLS procedure is applied to the results of the Rosenbrock test problem, and wing structural weight from the structural optimization of the HSCT. A nonsymmetric IRLS (NIRLS), utilizing one-sidedness of optimization errors, is more effective than IRLS in identifying outliers. Detection and repair of the outliers improve accuracy of the RS approximations. Finally, configuration optimizations of the HSCT are performed using the improved wing bending material weight RS models. / Ph. D.

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