As posições críticas dos estatísticos, que atuam em programas de melhoramento genético, referem-se à falta de uma análise criteriosa da estrutura da interação do genótipo com o ambiente (G x E) como um dos principais problemas para a recomendação de cultivares. Tradicionalmente, a análise dessa estrutura á superficial não detalhando os efeitos da complexidade da interação. Com isso, os ganhos genéticos podem ser diminutos, pela não seleção de genótipos superiores melhores indicados a um ambiente específico. A busca constante por novos métodos e algoritmos, visando eliminar ou minimizar esse problema, tem proporcionado uma inegável evolução científica, com a geração de tecnologias de ponta que envolvem grande capacidade de processamento computacional. Atualmente, a metodologia AMMI (additive main efects and multiplicative interaction analysis) propõe ser mais eficiente que as análises usuais na interpretação e compreensão da interação G x E. Entretanto, os principais pontos negativos dessa metodologia dizem respeito à dificuldade de se interpretar a interação quando há baixa explicação do primeiro componente principal; à dificuldade de se quantificar os escores como baixos, considerando estável os genótipos e/ou ambientes, além de não apresentar o padrão de resposta do genótipo, o que caracteriza os padrões de adaptabilidade. Nesse contexto, essa metodologia apresenta alguns inconvenientes de ordem estatística, fazendo com que suas interpretações sejam vistas com ressalvas. Assim, o objetivo desta tese foi o desenvolvimento de procedimentos estatísticos que minimizem esses problemas, tornando a metodologia AMMI mais precisa e confiável na caracterização da estabilidade e adaptabilidade fenotípica de plantas. Nesse sentido, foi desenvolvido uma metodologia via reamostragem "bootstrap", no modelo AMMI, que possibilitou as análises gráficas e numéricas, das estabilidades e adaptabilidades fenotípicas de 75 progênies de Eucalyptus grandis, procedentes de três localidades australianas, e implantadas em sete testes de procedências e progênies nas regiões Sul e Sudeste do Brasil. Os resultados indicaram comportamentos diferenciados dos genótipos e dos ambientes, sendo a interação G x E significativa ao nível de 1% de probabilidade. As interpretações das estabilidades e adaptabilidades fenotípicas foram melhores compreendidas com a realização da reamostragem "bootstrap". A metodologia "bootstrap" AMMI, eliminou as dúvidas relacionadas à quantificação dos escores como baixos, tornando a metodologia AMMI mais precisa e confiável, na predição da estabilidade fenotípica de genótipos e de ambientes. O coeficiente "bootstrap" de estabilidade (CBE), baseado na distância quadrada de Mahalanobis, sobre o modelo AMMI2, obtidos através da região de predição para o vetor nulo, permitiu classificar os genótipos e ambientes em cinco escalas de estabilidade, e, conjuntamente com as representações gráficas das regiões de confiança para a estabilidade e gráficos de dispersões dos escores bootstrap", em biplot AMMI2, apresentaram melhores qualidades para predições das estabilidades fenotípicas, do que o método tradicional AMMI, com representação gráfica em biplot. / Reliable evaluation of the stability of genotypes and environment is of prime concern to plant breeders, who have Undertaken much research into the development of methods for studying in detail the structure of genotype-environment interaction. The lack of a comprehensive analysis of the structure of the GEI interaction has been a stumbling block to the recommendation of cultivars. Traditionally, the analysis of that structure was superficial and stopped short of detailing the efects of the complexity of the interaction. However, recent advances in computer science have allowed the development of interactive systems of data processing with fast and precise algorithms. Consequently, statistical methods are being developed to study in detail the structure and stability of GEI interaction. At the moment, the Additive Main Efects and Multiplicative Interaction (AMMI) Model promises to be more eficient than the usual analyses in the interpretation and understanding of the GEI interaction. The main drawbacks of the AMMI methodology are the dificulty of interpreting the interaction when there is a poor explanation of the first principal component; the dificulty of determining low scores, which relates to the statistical stability of the genotypes and/or environments; and the lack of presentation of the pattern of response of the genotype, which characterizes the adaptability patterns of the groups formed through significant parameters. Thus care needs to be exercised in the interpretation. The present contribution proposes the use of bootstrap re-sampling in the AMMI Model, and applies it to obtain both a graphical and a numerical analysis of the phenotypic stability and adaptability of 75 progenies of Eucalyptus grandis from Australia that were planted in seven environments in the South and Southeast regions of Brazil. The results show diderential behavior of genotypes and environments, the genotype x environment interaction being significant (p value < 0.01). The interpretation of the phenotypic stability through graphical analysis of the AMMI biplot is better understood with the aid of the bootstrap. The bootstrap coeficient of stability based on the squared Mahalanobis distance of the scores bootstrap, shows that genotypes and environments can be diferentiated in terms of their stabilities. The AMMI bootstrap proposal thus provides better and more precise predictions of phenotypic stability and adaptability of the geno- types than the traditional AMMI analysis, and eliminates the doubts related to the identification of the low scores.

Classification approaches are used in many areas in order to identify or estimate classes, which different observations belong to. The classification approach, Mahalanobis Taguchi System (MTS) is analyzed and further improved for multi-class classification problems under the scope of this thesis study. MTS tries to explore significant variables and classify a new observation based on its Mahalanobis distance (MD). In this study, first, sample size problems, which are encountered mostly in small data sets, and multicollinearity problems, which constitute some limitations of MTS, are analyzed and a re-sampling approach is explored as a solution. Our re-sampling approach, which only works for data sets with two classes, is a combination of over-sampling and under-sampling. Over-sampling is based on SMOTE, which generates the synthetic observations between the nearest neighbors of observations in the minority class. In addition, MTS models are used to test the performance of several re-sampling parameters, for which the most appropriate values are sought specific to each case. In the second part, multi-class classification methods with MTS are developed. An algorithm, namely Feature Weighted Multi-class MTS-I (FWMMTS-I), is inspired by the descent feature weighted MD. It relaxes adding up of the MDs for variables equally. This provides representations of noisy variables with weights close to zero so that they do not mask the other variables. As a second multi-class classification algorithm, the original MTS method is extended to multi-class problems, which is called Multi-class MTS (MMTS). In addition, a comparable approach to that of Su and Hsiao (2009), which also considers weights of variables, is studied with a modification in MD calculation. It is named as Feature Weighted Multi-class MTS-II (FWMMTS-II). The methods are compared on eight different multi-class data sets using a 5-fold stratified cross validation approach. Results show that FWMMTS-I is as accurate as MMTS, and they are better than FWMMTS-II. Interestingly, the Mahalanobis Distance Classifier (MDC) using all the variables directly in the classification model has performed equally well on the studied data sets.

As posições críticas dos estatísticos, que atuam em programas de melhoramento genético, referem-se à falta de uma análise criteriosa da estrutura da interação do genótipo com o ambiente (G x E) como um dos principais problemas para a recomendação de cultivares. Tradicionalmente, a análise dessa estrutura á superficial não detalhando os efeitos da complexidade da interação. Com isso, os ganhos genéticos podem ser diminutos, pela não seleção de genótipos superiores melhores indicados a um ambiente específico. A busca constante por novos métodos e algoritmos, visando eliminar ou minimizar esse problema, tem proporcionado uma inegável evolução científica, com a geração de tecnologias de ponta que envolvem grande capacidade de processamento computacional. Atualmente, a metodologia AMMI (additive main efects and multiplicative interaction analysis) propõe ser mais eficiente que as análises usuais na interpretação e compreensão da interação G x E. Entretanto, os principais pontos negativos dessa metodologia dizem respeito à dificuldade de se interpretar a interação quando há baixa explicação do primeiro componente principal; à dificuldade de se quantificar os escores como baixos, considerando estável os genótipos e/ou ambientes, além de não apresentar o padrão de resposta do genótipo, o que caracteriza os padrões de adaptabilidade. Nesse contexto, essa metodologia apresenta alguns inconvenientes de ordem estatística, fazendo com que suas interpretações sejam vistas com ressalvas. Assim, o objetivo desta tese foi o desenvolvimento de procedimentos estatísticos que minimizem esses problemas, tornando a metodologia AMMI mais precisa e confiável na caracterização da estabilidade e adaptabilidade fenotípica de plantas. Nesse sentido, foi desenvolvido uma metodologia via reamostragem "bootstrap", no modelo AMMI, que possibilitou as análises gráficas e numéricas, das estabilidades e adaptabilidades fenotípicas de 75 progênies de Eucalyptus grandis, procedentes de três localidades australianas, e implantadas em sete testes de procedências e progênies nas regiões Sul e Sudeste do Brasil. Os resultados indicaram comportamentos diferenciados dos genótipos e dos ambientes, sendo a interação G x E significativa ao nível de 1% de probabilidade. As interpretações das estabilidades e adaptabilidades fenotípicas foram melhores compreendidas com a realização da reamostragem "bootstrap". A metodologia "bootstrap" AMMI, eliminou as dúvidas relacionadas à quantificação dos escores como baixos, tornando a metodologia AMMI mais precisa e confiável, na predição da estabilidade fenotípica de genótipos e de ambientes. O coeficiente "bootstrap" de estabilidade (CBE), baseado na distância quadrada de Mahalanobis, sobre o modelo AMMI2, obtidos através da região de predição para o vetor nulo, permitiu classificar os genótipos e ambientes em cinco escalas de estabilidade, e, conjuntamente com as representações gráficas das regiões de confiança para a estabilidade e gráficos de dispersões dos escores bootstrap", em biplot AMMI2, apresentaram melhores qualidades para predições das estabilidades fenotípicas, do que o método tradicional AMMI, com representação gráfica em biplot. / Reliable evaluation of the stability of genotypes and environment is of prime concern to plant breeders, who have Undertaken much research into the development of methods for studying in detail the structure of genotype-environment interaction. The lack of a comprehensive analysis of the structure of the GEI interaction has been a stumbling block to the recommendation of cultivars. Traditionally, the analysis of that structure was superficial and stopped short of detailing the efects of the complexity of the interaction. However, recent advances in computer science have allowed the development of interactive systems of data processing with fast and precise algorithms. Consequently, statistical methods are being developed to study in detail the structure and stability of GEI interaction. At the moment, the Additive Main Efects and Multiplicative Interaction (AMMI) Model promises to be more eficient than the usual analyses in the interpretation and understanding of the GEI interaction. The main drawbacks of the AMMI methodology are the dificulty of interpreting the interaction when there is a poor explanation of the first principal component; the dificulty of determining low scores, which relates to the statistical stability of the genotypes and/or environments; and the lack of presentation of the pattern of response of the genotype, which characterizes the adaptability patterns of the groups formed through significant parameters. Thus care needs to be exercised in the interpretation. The present contribution proposes the use of bootstrap re-sampling in the AMMI Model, and applies it to obtain both a graphical and a numerical analysis of the phenotypic stability and adaptability of 75 progenies of Eucalyptus grandis from Australia that were planted in seven environments in the South and Southeast regions of Brazil. The results show diderential behavior of genotypes and environments, the genotype x environment interaction being significant (p value < 0.01). The interpretation of the phenotypic stability through graphical analysis of the AMMI biplot is better understood with the aid of the bootstrap. The bootstrap coeficient of stability based on the squared Mahalanobis distance of the scores bootstrap, shows that genotypes and environments can be diferentiated in terms of their stabilities. The AMMI bootstrap proposal thus provides better and more precise predictions of phenotypic stability and adaptability of the geno- types than the traditional AMMI analysis, and eliminates the doubts related to the identification of the low scores.

<p>Statistical modeling aims at constructing a mathematical model for an existing data set. As a comprehensive concept, statistical modeling leads to a wide range of interesting problems. Modern parametric models, such as deepnets, have achieved remarkable success in quite a few application areas with massive data. Although being powerful in practice, many fitted over-parameterized models potentially suffer from losing good statistical properties. For this reason, a new framework named the Auto-modeling (AM) framework is proposed. Philosophically, the mindset is to fit models to future observations rather than the observed sample. Technically, choosing an imputation model for generating future observations, we fit models to future observations via optimizing an approximation to the desired expected loss function based on its sample counterpart and what we call an adaptive {\it duality function}.</p> <p><br></p> <p>The first part of the dissertation (Chapter 2 to 7) focuses on the new philosophical perspective of the method, as well as the details of the main framework. Technical details, including essential theoretical properties of the method are also investigated. We also demonstrate the superior performance of the proposed method via three applications: Many-normal-means problem, $n < p$ linear regression and image classification.</p> <p><br></p> <p>The second part of the dissertation (Chapter 8) focuses on the application of the AM framework to the construction of linear regression models. Our primary objective is to shed light on the stability issue associated with the commonly used data-driven model selection methods such as cross-validation (CV). Furthermore, we highlight the philosophical distinctions between CV and AM. Theoretical properties and numerical examples presented in the study demonstrate the potential and promise of AM-based linear model selection. Additionally, we have devised a conformal prediction method specifically tailored for quantifying the uncertainty of AM predictions in the context of linear regression.</p>

Les systèmes embarqués temps réel critiques intègrent des architectures complexes qui évoluent constamment afin d'intégrer des nouvelles fonctionnalités requises par les utilisateurs finaux des systèmes (automobile, avionique, ferroviaire, etc.). Ces nouvelles architectures ont un impact direct sur la variabilité du comportement temporel des systèmes temps réel. Cette variabilité entraîne un sur-approvisionnement important si la conception du système est uniquement basée sur le raisonnement pire cas. Approches probabilistes proposent des solutions basées sur la probabilité d'occurrence des valeurs les plus défavorables afin d'éviter le sur-approvisionnement, tout en satisfaisant les contraintes temps réel. Les principaux objectifs de ce travail sont de proposer des nouvelles techniques d'analyse des systèmes temps réel probabilistes et des moyens de diminuer la complexité de ces analyses, ainsi que de proposer des algorithmes optimaux d'ordonnancement à priorité fixe pour les systèmes avec des temps d'exécution décrits par des variables aléatoires. Les résultats que nous présentons dans ce travail ont été prouvés surs et à utiliser pour les systèmes temps réel durs, qui sont l'objet principal de notre travail. Notre analyse des systèmes avec plusieurs paramètres probabilistes a été démontrée considérablement moins pessimiste que d'autres types d'analyses. Cet analyse combinée avec des algorithmes d'ordonnancement optimaux appropriées pour les systèmes temps réel probabilistes peut aider les concepteurs de systèmes à mieux apprécier la faisabilité d'un système, en particulier de ceux qui sont jugé irréalisable par des analyses/algorithmes d'ordonnancement déterministes / Critical real-time embedded systems integrate complex architectures that evolve constantly in order to provide new functionality required by the end users of the systems (automotive, avionics, railway, etc). These new architectures have a direct impact on the variability of the timing behavior of the real-time system. This variability leads to important over-provisioning if the design of the system is based only on worst case reasoning. Probabilistic approaches propose solutions are based on the probability of occurrence of the worst case values in order to avoid over provisioning while satisfying real-time constraints. The main objectives of this work are new analysis techniques for probabilistic real-time systems and ways of decreasing the complexity of these analyses, as well as to propose optimal fixed priority scheduling algorithms for systems that have variability at the level of execution times. The results that we provide in this work have been proved applicable to hard real-time systems, which are the main focus of our work. Our proposed analysis for systems with multiple probabilistic parameters has been shown to greatly decrease the pessimism introduced by other types of analyses. This type of analysis combined with the proper optimal scheduling algorithms for probabilistic real-time system help the system designers to better appreciate the feasibility of a system, especially of those that are deemed unfeasible by deterministic analyses/scheduling algorithms