The content of this dissertation is divided into two main topics: 1) nonlinear profile monitoring and 2) an improved approximate distribution for the T² statistic based on the successive differences covariance matrix estimator. Part 1: Nonlinear Profile Monitoring In an increasing number of cases the quality of a product or process cannot adequately be represented by the distribution of a univariate quality variable or the multivariate distribution of a vector of quality variables. Rather, a series of measurements are taken across some continuum, such as time or space, to create a profile. The profile determines the product quality at that sampling period. We propose Phase I methods to analyze profiles in a baseline dataset where the profiles can be modeled through either a parametric nonlinear regression function or a nonparametric regression function. We illustrate our methods using data from Walker and Wright (2002) and from dose-response data from DuPont Crop Protection. Part 2: Approximate Distribution of T² Although the T² statistic based on the successive differences estimator has been shown to be effective in detecting a shift in the mean vector (Sullivan and Woodall (1996) and Vargas (2003)), the exact distribution of this statistic is unknown. An accurate upper control limit (UCL) for the T² chart based on this statistic depends on knowing its distribution. Two approximate distributions have been proposed in the literature. We demonstrate the inadequacy of these two approximations and derive useful properties of this statistic. We give an improved approximate distribution and recommendations for its use. / Ph. D.

In this thesis the two disciplines of Statistics and Artificial Neural Networks are combined into an integrated study of a data set of a weather modification Experiment. An extensive literature study on artificial neural network methodology has revealed the strongly interdisciplinary nature of the research and the applications in this field. An artificial neural networks are becoming increasingly popular with data analysts, statisticians are becoming more involved in the field. A recursive algoritlun is developed to optimize the number of hidden nodes in a feedforward artificial neural network to demonstrate how existing statistical techniques such as nonlinear regression and the likelihood-ratio test can be applied in innovative ways to develop and refine neural network methodology. This pruning algorithm is an original contribution to the field of artificial neural network methodology that simplifies the process of architecture selection, thereby reducing the number of training sessions that is needed to find a model that fits the data adequately. [n addition, a statistical model to classify weather modification data is developed using both a feedforward multilayer perceptron artificial neural network and a discriminant analysis. The two models are compared and the effectiveness of applying an artificial neural network model to a relatively small data set assessed. The formulation of the problem, the approach that has been followed to solve it and the novel modelling application all combine to make an original contribution to the interdisciplinary fields of Statistics and Artificial Neural Networks as well as to the discipline of meteorology. / Mathematical Sciences / D. Phil. (Statistics)

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In this thesis the two disciplines of Statistics and Artificial Neural Networks are combined into an integrated study of a data set of a weather modification Experiment. An extensive literature study on artificial neural network methodology has revealed the strongly interdisciplinary nature of the research and the applications in this field. An artificial neural networks are becoming increasingly popular with data analysts, statisticians are becoming more involved in the field. A recursive algoritlun is developed to optimize the number of hidden nodes in a feedforward artificial neural network to demonstrate how existing statistical techniques such as nonlinear regression and the likelihood-ratio test can be applied in innovative ways to develop and refine neural network methodology. This pruning algorithm is an original contribution to the field of artificial neural network methodology that simplifies the process of architecture selection, thereby reducing the number of training sessions that is needed to find a model that fits the data adequately. [n addition, a statistical model to classify weather modification data is developed using both a feedforward multilayer perceptron artificial neural network and a discriminant analysis. The two models are compared and the effectiveness of applying an artificial neural network model to a relatively small data set assessed. The formulation of the problem, the approach that has been followed to solve it and the novel modelling application all combine to make an original contribution to the interdisciplinary fields of Statistics and Artificial Neural Networks as well as to the discipline of meteorology. / Mathematical Sciences / D. Phil. (Statistics)

The issue of this master's thesis is a creation of new prediction unit for existing system of knowledge discovery in database. The first part of project deal with general problems of knowledge discovery in database and predictive analysis. The second part of the project deal with system developed on FIT, for which is module implemented, used technologies, concept and implementation of mining module for this system. The solution is implemented in Java language and is a built on the NetBeans platform.

This bachelor thesis is written for KTH Royal Institute of Technology and Ymer Technology AB. It examines the friction factor associated with the pressure drop in wavy-fin heat exchangers. Previous studies have used a nonlinear approach for determining the regression coefficients. This study introduces a linearizing transform that solves the issues of finding non-optimal parameter values stemming from the current nonlinear approach. The linearization also drastically improves the computational time. A final model explaining 95.4\% of the variance in the data is presented. Methods for avoiding overfitting, detecting outliers and hidden extrapolation are presented and used to evaluate the model. The implications of the mathematical results on improving profit, competitiveness, and customer relationships are analyzed in the second part of the report with a qualitative approach. / Denna kandidatuppsats är skrivet vid Kungliga Tekniska Högskolan och Ymer Technology AB. Det undersöker den friktionsfaktor som associeras med tryckfallet i kylare med wavy-fins. Tidigare studier har använt ett ickelinjärt tillvägagångssätt för att bestämma regressionskoefficienterna. Denna studie introducerar en linjäriserande transform som löser problemen med att hitta icke-optimala paramatervärden, som härstammar från tidigare icke-linjära tillvägagångsätt. Linjäriseringen visar sig även förbättra beräkningstiden drastiskt. En slutgiltig modell som förklarar 95\% av variansen i datan presenteras. Metoder för att undvika overfitting, identifiera outliers, och undvika att falla offer för gömd extrapolation presenteras och används för att evaluera modellen. De matematiska resultatens implikationer för Ymer med avseende på vinst, konkurrenskraft och kundrelationer, analyseras i den andra delen av rapporten med en kvalitativ ansats.

The aim of this work is to present an inference and diagnostic study of an extension of the lifetime distribution family proposed by Birnbaum and Saunders (1969a,b). This extension is obtained by considering a skew-elliptical distribution instead of the normal distribution. Specifically, in this work we develop a Birnbaum-Saunders (BS) distribution type based on scale mixtures of skew-normal distributions (SMSN). The resulting family of lifetime distributions represents a robust extension of the usual BS distribution. Based on this family, we reproduce the usual properties of the BS distribution, and present an estimation method based on the EM algorithm. In addition, we present regression models associated with the BS distributions (based on scale mixtures of skew-normal), which are developed as an extension of the sinh-normal distribution (Rieck and Nedelman, 1991). For this model we consider an estimation and diagnostic study for uncensored data. / O objetivo deste trabalho é apresentar um estudo de inferência e diagnóstico em uma extensão da família de distribuições de tempos de vida proposta por Birnbaum e Saunders (1969a,b). Esta extensão é obtida ao considerar uma distribuição skew-elíptica em lugar da distribuição normal. Especificamente, neste trabalho desenvolveremos um tipo de distribuição Birnbaum-Saunders (BS) baseda nas distribuições mistura de escala skew-normal (MESN). Esta família resultante de distribuições de tempos de vida representa uma extensão robusta da distribuição BS usual. Baseado nesta família, vamos reproduzir as propriedades usuais da distribuição BS, e apresentar um método de estimação baseado no algoritmo EM. Além disso, vamos apresentar modelos de regressão associado à distribuições BS (baseada na distribuição mistura de escala skew-normal), que é desenvolvida como uma extensão da distribuição senh-normal (Rieck e Nedelman, 1991), para estes vamos considerar um estudo de estimação e diagnóstisco para dados sem censura.

L’imagerie et la spectroscopie par résonance magnétique nucléaire (IRM et SRM) sont des méthodes non-invasives qui ont le potentiel d’estimer in vivo la quantité et la qualité des adiposités abdominales. Le contexte scientifique et clinique de ce manuscrit s’articule autour de l’étude de surnutrition « Poly-Nut » dont l’un des objectifs est d’analyser les évolutions des tissus adipeux (TA) dans une phase rapide de prise de poids. L’originalité et la complexité de cette thèse résident dans le développement, l’adaptation et la comparaison de plusieurs méthodes quantitatives d’IRM et de SRM, pour l’étude du signal lipidique dans un contexte clinique à 3T. La fiabilité et la validation des mesures obtenues in vivo par ces techniques font ici l’objet d’une étude approfondie. Pour l’analyse quantitative du signal de spectroscopie, différentes méthodes existantes ont été comparées à celle développée spécifiquement pour notre étude clinique. L’estimation paramétrique par moindres carrés non linéaires appliquée aux spectres RMN des lipides peut conduire, selon la fonction modèle utilisée, à un problème non linéaire mal posé. Nous montrons alors que l’utilisation d’un modèle simplifié se fondant sur la structure d’une chaine de triglycéride, comme utilisé récemment en imagerie quantitative, constitue une solution valide au regard de l’état de l’art. Ensuite différentes méthodes (IRM, SRM, Dual Energy X-ray absorptiometry, chromatographie en phase gazeuse) ont été utilisées pour caractériser les TA sous-cutanés et viscéraux. Le suivi par IRM du contenu lipidique du foie ainsi que du volume et de la composition en acide gras des TA à partir d’une unique acquisition en multi-écho de gradient est démontré. Enfin des développements expérimentaux menés parallèlement à l’étude clinique sur un imageur préclinique à 4,7T, comparent différentes stratégies d’encodage du déplacement chimique par imagerie et caractérisent des méthodes SRM pour estimer in vivo la proportion d’omégas-3 dans les chaînes d’acides gras. / Magnetic resonance imaging and spectroscopy (MRI and MRS) are non-invasive methods that have the potential to estimate in vivo the quantity and the quality of abdominal adipose tissues (AT). The scientific and clinical context of this thesis is based on an overfeeding study entitled "Poly-Nut". One of the main objectives of this study is to analyze changes in adipose tissues in a rapid phase of weight gain. The originality and complexity of this thesis rely in the development, adaptation and comparison of several quantitative methods of MRI and MRS, for the study of lipid signal, in a clinical context, at 3T. The reliability and the validation of the measurements obtained in vivo using these techniques are the main subject of this PhD thesis. For the quantitative analysis of the spectroscopy signal, different existing methods have been compared to those developed specifically for our clinical study. According to the model function used, the nonlinear-least-squares parametric estimation applied to the lipid spectra can lead to an ill-posed nonlinear problem. We demonstrated that the use of a simplified model based on the structure of a triglyceride chain, as recently used in quantitative imaging, was a valid solution regarding the state of the art. Then different methods (MRI, MRS, Dual Energy X-ray absorptiometry, gas chromatography) were used to characterize the subcutaneous and visceral AT. We demonstrated the feasibility of MRI to follow the lipid content in the liver as well as the volume and the fatty acid composition of AT using a single multiple gradient-echo acquisition. Finally, experimental developments were carried out in parallel with the clinical study, on a 4.7T preclinical system, first, to compare different strategies for encoding the chemical shift using imaging and, secondly, to characterize MRS methods for in vivo estimation of the relative proportion of omega-3 among all fatty acids.

Cette thèse construit un modèle théorique qui renouvelle l’approche traditionnelle de l’équilibre du marché. En introduisant dans le paradigme néo-classique le principe de préférence pour la quantité, il génère de façon optimale des stocks dans un marché concurrentiel. Les résultats sont très importants, car ils expliquent à la fois l’émergence des invendus et l’existence de cycles économiques. En outre, il étudie le comportement optimal du monopole dont la puissance de marché dépend non seulement de la quantité de biens étalés, mais aussi de celle de biens achetés. Contrairement à l’hypothèse traditionnelle selon laquelle le monopoleur choisit le prix ou la quantité qui maximise son profit, il attire, via un indice de Lerner généralisé la demande à la fois par le prix et la quantité de biens exposés. Quelle que soit la structure du marché, le phénomène d’accumulation des stocks de biens apparaît dans l’économie. De plus, il a l’avantage d’expliquer explicitement les achats impulsifs non encore traités par la théorie économique. Pour vérifier la robustesse des résultats du modèle théorique, ils sont testés sur des données américaines. En raison de leur non-linéarité, la méthode de Gauss-Newton est appropriée pour analyser l’impact de la préférence pour la quantité sur la production et l’accumulation de biens, et par conséquent sur les prévisions de PIB. Enfin, cette thèse construit un modèle à générations imbriquées à deux pays qui étend l’équilibre dynamique à un gamma-équilibre dynamique sans friction. Sur la base de la contrainte de détention préalable d’encaisse, il ressort les conditions de sur-accumulation du capital et les conséquences de la mobilité du capital sur le bien-être dans un contexte d’accumulation du stock d’invendus / This thesis constructs a theoretical model that renews the traditional approach of the market equilibrium. By introducing into the neoclassical paradigm the principle of preference for quantity, it optimally generates inventories within a competitive market. The results are very important since they explain both the emergence of unsold goods and the existence of economic cycles. In addition, it studies the optimal behavior of a monopolist whose the market power depends not only on the quantity of displayed goods but also that of goods that the main consumer is willing to buy. Contrary to the traditional assumption that the monopolist chooses price or quantity that maximizes its profit, through a generalized Lerner index (GLI) it attracts customers’ demand by both the price and the quantity of displayed goods. Whatever the market structure, the phenomenon of inventory accumulation appears in the economy. Furthermore, it has the advantage of explicitly explaining impulse purchases untreated by economics. To check the robustness of the results,the theoretical model is fitted to U.S. data. Due to its nonlinearity, the Gauss-Newtonmethod is appropriate to highlight the impact of consumers’ preference for quantity on production and accumulation of goods and consequently GDP forecast. Finally, this thesis builds a two-country overlapping generations (OLG) model which extends the dynamic OLG equilibrium to a frictionless dynamic OLG gamma-equilibrium. Based on the cash-inadvance constraint, it highlights the conditions of over-accumulation of capital and welfare implications of capital mobility in a context of accumulation of stock of unsold goods.

The aim of this work is to present an inference and diagnostic study of an extension of the lifetime distribution family proposed by Birnbaum and Saunders (1969a,b). This extension is obtained by considering a skew-elliptical distribution instead of the normal distribution. Specifically, in this work we develop a Birnbaum-Saunders (BS) distribution type based on scale mixtures of skew-normal distributions (SMSN). The resulting family of lifetime distributions represents a robust extension of the usual BS distribution. Based on this family, we reproduce the usual properties of the BS distribution, and present an estimation method based on the EM algorithm. In addition, we present regression models associated with the BS distributions (based on scale mixtures of skew-normal), which are developed as an extension of the sinh-normal distribution (Rieck and Nedelman, 1991). For this model we consider an estimation and diagnostic study for uncensored data. / O objetivo deste trabalho é apresentar um estudo de inferência e diagnóstico em uma extensão da família de distribuições de tempos de vida proposta por Birnbaum e Saunders (1969a,b). Esta extensão é obtida ao considerar uma distribuição skew-elíptica em lugar da distribuição normal. Especificamente, neste trabalho desenvolveremos um tipo de distribuição Birnbaum-Saunders (BS) baseda nas distribuições mistura de escala skew-normal (MESN). Esta família resultante de distribuições de tempos de vida representa uma extensão robusta da distribuição BS usual. Baseado nesta família, vamos reproduzir as propriedades usuais da distribuição BS, e apresentar um método de estimação baseado no algoritmo EM. Além disso, vamos apresentar modelos de regressão associado à distribuições BS (baseada na distribuição mistura de escala skew-normal), que é desenvolvida como uma extensão da distribuição senh-normal (Rieck e Nedelman, 1991), para estes vamos considerar um estudo de estimação e diagnóstisco para dados sem censura.