Nesta tese consideramos um modelo de regressão não paramétrica, quando a variável explicativa e um processo estritamente estacionário e alpha-mixing. São estudadas as condições sobre o processo Xt e sua estrutura de dependência, assim como do domínio da função f a ser estimada. Também são feitas as adaptações necessárias aos procedimentos para obter as taxas de convergência do risco para a norma Lp, no caso de ondaletas deformadas. Em relação às ondaletas adaptativas de Haar, obtêm-se as taxas de convergência do risco do estimador proposto. Mediante estudos de simulação, e avaliado o desempenho dos procedimentos propostos quando aplicados a amostras finitas sob diferentes níveis de perturbação do sinal e diferentes tamanhos da amostra. Também são feitas aplicações a dados reais. / In this thesis we consider a nonparametric regression model, when the exploratory variables are alpha-mixing stationary processes. We obtain convergence rates for risk for Lp norm, via warped wavelets, under suitable regularity conditions. For estimation using design adapted Haar wavelets we obtain convergence rates for the risk of the proposed estimator. The performance of the estimators are assessed via simulation studies with dierent sample sizes and dierent signal-to-noise ratios. Applications to real data are also given.

Nesta tese consideramos um modelo de regressão não paramétrica, quando a variável explicativa e um processo estritamente estacionário e alpha-mixing. São estudadas as condições sobre o processo Xt e sua estrutura de dependência, assim como do domínio da função f a ser estimada. Também são feitas as adaptações necessárias aos procedimentos para obter as taxas de convergência do risco para a norma Lp, no caso de ondaletas deformadas. Em relação às ondaletas adaptativas de Haar, obtêm-se as taxas de convergência do risco do estimador proposto. Mediante estudos de simulação, e avaliado o desempenho dos procedimentos propostos quando aplicados a amostras finitas sob diferentes níveis de perturbação do sinal e diferentes tamanhos da amostra. Também são feitas aplicações a dados reais. / In this thesis we consider a nonparametric regression model, when the exploratory variables are alpha-mixing stationary processes. We obtain convergence rates for risk for Lp norm, via warped wavelets, under suitable regularity conditions. For estimation using design adapted Haar wavelets we obtain convergence rates for the risk of the proposed estimator. The performance of the estimators are assessed via simulation studies with dierent sample sizes and dierent signal-to-noise ratios. Applications to real data are also given.

Cette thèse proposée utilise les ondelettes de Haar à créer de nouveaux indicateurs techniques, d’en évaluer leurs performances afin de tester la validité de l’efficience faible des marchés financiers. L’approche choisie vise à mettre en œuvre les capacités des indicateurs techniques à capter la mémoire longue présente dans les indices boursiers américains et européens à travers l’estimation de la tendance par le processus de lissage. De plus, cette dernière est une composante importante dans les séries économiques et financières. En effet, elle a fait l’objet d’innombrables investigations tant en analyse technique, qu’en traitement du signal et dans la théorie des cycles économiques. Toutefois, sa présence n’entre pas en ligne de compte dans la théorie classique de la finance, car les principaux modèles utilisés se focalisent sur les variations des cours boursiers. À cet effet, la tendance constitue une source de non-stationnarité entraînant des difficultés majeures pour la modélisation économétrique ou financière. Exploiter cette tendance s’affranchit, dans ce cas, des hypothèses de non-stationnarité tendancielle ou de racine unitaire. En plus, à l’issue des résultats que nous avons obtenus à partir du modèle à changement de régime. Nous confirmons qu’il est possible d’exploiter la présence de mémoire longue dans les cours, et également de battre le marché en présence de coûts de transactions sur les marchés américains et européens. / This proposed thesis uses the Haar wavelets to create new technical indicators, to evaluate their performance in order to test the validity of the weak form of efficient market hypothesis. The chosen approach aims to implement the capabilities of technical indicators to capture the long memory present in the US and European stock indices through the estimation of the trend by the smoothing process. Moreover, the trend is an important component in the economic and financial series. Indeed, it has been the subject of innumerable investigations in technical analysis, in signal processing and in the theory business cycle theory. However, its presence is not taken into account in the classic theory of finance because the main models used focus on changes in stock prices. For this purpose, the trend constitutes a source of non-stationarity leading to major difficulties for econometric or financial modeling. Exploit trend is freed, in this case, from the hypotheses of tendancy or unit root. In addition, the issue of the results we obtained from the regime change model. We confirm that it is possible to exploit the presence of long memory in the series, and also to beat the market in the presence of transaction costs on the American and European markets.

Cette thèse traite de l’analyse robuste du comportement dynamique des systèmes frottants. Ces derniers constituent une classe particulière des systèmes non linéaires et sont caractérisés par des comportements dynamiques très sensibles aux variations des paramètres de conception en particulier aux dispersions des lois de frottement. Cette sensibilité se traduit par des variations qualitatives importantes du comportement dynamique (stabilité, niveaux vibratoire) qui peuvent alors affecter négativement les performances des systèmes frottants. Il est ainsi important, voire indispensable, de pouvoir tenir compte de la dispersion des lois de frottement dans l’étude et l’analyse du comportement dynamique des systèmes frottants afin d’en garantir la robustesse et, dans une perspective plus générale, d’asseoir une démarche de conception robuste des systèmes frottants. Des méthodes spectrales basées sur le concept du chaos polynomial sont proposées dans cette thèse pour traiter de l’analyse robuste du comportement dynamique des systèmes frottants. Pouvant modéliser les fonctions et processus stochastiques, ces méthodes sont adaptées au problème en particulier à l’analyse de la stabilité et à la prédiction des niveaux vibratoires en tenant compte de la dispersion des lois de frottement. Différentes procédures sont proposées et développées pour traiter de ces deux questions. Une efficacité importante a été illustrée à travers l’évaluation des différentes méthodes proposées (chaos polynomial généralisé, chaos polynomial multi-éléments, chaos de Wiener-Haar) en les appliquant sur un exemple de système frottant. En effet, il est montré que ces méthodes offrent une alternative très intéressante à la méthode prohibitive, mais référentielle, de Monte Carlo puisque, pour des niveaux de précision et de confiance similaires, le coût en nombre, en volume et nécessairement en temps de calcul occasionné par les méthodes spectrales sur les différentes analyses (de la stabilité et des niveaux vibratoire) est largement inférieur à celui requis par la technique de Monte Carlo. / This thesis deals with the robust analysis of the dynamic behaviour of dry friction systems. These are a special class of nonlinear systems and are characterized by dynamic behaviors very sensitive to changes in design parameters in particular to dispersions of friction laws. This sensitivity results in important qualitative changes (stability, vibration levels) that can adversely affect the performances of friction systems. It is thus important, even essential, to take account of the dispersion laws of friction in the study and analysis of the dynamic behavior of friction systems in order to ensure robustness and, in a more general perspective, to establish a robust design approach for friction systems. Spectral methods based on the concept of polynomial chaos are proposed in this thesis to address these problems. The spectral methods can model random functions and stochastic processes so they have been adapted to deal with the robust analysis of the dynamic behavior of frictions systems subjected to random friction coefficient. Different procedures are proposed and developed to, analyze with robustness the stability of friction system in a first step and to predict and estimate the vibratory levels of the same systems. High efficiency is demonstrated by evaluating the various proposed methods (generalized polynomial chaos, multi-element polynomial chaos, Wiener-Haar chaos) on the two issues considered. Indeed, it is shown that these methods offer an attractive alternative to the prohibitive, but referential, Monte Carlo method since, for similar levels of accuracy and confidence, the cost in terms of number and volume of calculus and thus in time of computing occasioned by the spectral methods on the different problems (robust stability and vibration levels analysis) is well lower than the one occasioned by the Monte Carlo technique.

This master’s Thesis focuses on image processing on Android platform and development of an application, that is able to do face detection and recognition in real scene. Thesis gives highlight of modern algorithms of face detection. It first examines and compares the standard features of Android platform (FaceDetector a FaceDetectionListener) and JJIL, OpenIMAJ, OpenCV libraries experiment, and presents the results. For purposes of face recognition was selected OpenCV library. Three different algorithms of identification were tested: FisherFaces, EigenFaces a Local Binary Patterns Histograms. Based on performance comparison best methods were implemented in developed application.