This thesis contributes to the theoretical work on decision and game theory when decision makers or players perceive ambiguity. The first article introduces a new axiomatic framework for ambiguity aversion and provides axiomatic characterizations for important preference classes that thus far had lacked characterizations. The second article introduces a new axiom called Weak Monotonicity which is shown to play a crucial role in the multiple prior model. It is shown that for many important preference classes, the assumption of monotonic preferences is a consequence of the other axioms and does not have to be assumed. The third article introduces an intuitive definition of perceived ambiguity in the multiple prior model. It is shown that the approach allows an application to games where players perceive strategic ambiguity. A very general equilibrium existence result is given. The modelling capabilities of the approach are highlighted through the analysis of examples. The fourth article applies the model from the previous article to a specific class of games with a lattice-structure. We perform comparative statics on perceived ambiguity and ambiguity attitude. We show that more optimism does not necessarily lead to higher equilibria when players have Alpha-Maxmin preferences. We present necessary and sufficient conditions on the structure of the prior sets for this comparative statics result to hold. The introductory chapter provides the basis of the four articles in this thesis. An overview of axiomatic decision theory, decision-making under ambiguity and ambiguous games is given. It introduces and discusses the most relevant results from the literature.

On considère des jeux stochastiques joués sur un graphe fini. La première partie s’intéresse aux jeux stochastiques à deux joueurs et information parfaite. Dans de tels jeux, les joueurs choisissent des actions dans ensemble fini, tour à tour, pour une durée infinie, produisant une histoire infinie. Le but du jeu est donné par une fonction d’utilité qui associe un réel à chaque histoire, la fonction est bornée et Borel-mesurable. Le premier joueur veut maximiser l’utilité espérée, et le deuxième joueur veut la minimiser. On démontre que si la fonction d’utilité est à la fois shift-invariant et submixing alors le jeu est semi-positionnel. C’est-à-dire le premier joueur a une stratégie optimale qui est déterministe et sans mémoire. Les deux joueurs ont information parfaite: ils choisissent leurs actions en ayant une connaissance parfaite de toute l’histoire. Dans la deuxième partie, on étudie des jeux de durée fini où le joueur protagoniste a zéro information. C’est-à-dire qu’il ne reçoit aucune information sur le déroulement du jeu, par conséquent sa stratégie est un mot fini sur l’ensemble des actions. Un automates probabiliste peut être considéré comme un tel jeu qui a un seul joueur. Tout d’abord, on compare deux classes d’automates probabilistes pour lesquelles le problème de valeur 1 est décidable: les automates leaktight et les automates simples. On prouve que la classe des automates simples est un sous-ensemble strict de la classe des automates leaktight. Puis, on considère des jeux semi-aveugles, qui sont des jeux à deux joueurs où le maximiseur a zéro information, et le minimiseur est parfaitement informé. On définit la classe des jeux semi-aveugles leaktight et on montre que le problème d’accessibilité maxmin est décidable sur cette classe. / We consider stochastic games that are played on finite graphs. The subject of the first part are two-player stochastic games with perfect information. In such games the two players take turns choosing actions from a finite set, for an infinite duration, resulting in an infinite play. The objective of the game is given by a Borel-measurable and bounded payoff function that maps infinite plays to real numbers. The first player wants to maximize the expected payoff, and the second player has the opposite objective, that of minimizing the expected payoff. We prove that if the payoff function is both shift-invariant and submixing then the game is half-positional. This means that the first player has an optimal strategy that is at the same time pure and memoryless. Both players have perfect information, so the actions are chosen based on the whole history. In the second part we study finite-duration games where the protagonist player has zero information. That is, he gets no feedback from the game and consequently his strategy is a finite word over the set of actions. Probabilistic finite automata can be seen as an example of such a game that has only a single player. First we compare two classes of probabilistic automata: leaktight automata and simple automata, for which the value 1 problem is known to be decidable. We prove that simple automata are a strict subset of leaktight automata. Then we consider half-blind games, which are two player games where the maximizer has zero information and the minimizer is perfectly informed. We define the class of leaktight half-blind games and prove that it has a decidable maxmin reachability problem.

La céramique est l'un des matériaux archéologiques les plus importants pour aider à la reconstruction des civilisations passées. Les informations à propos des objets céramiques complexes incluent des données textuelles, numériques et multimédias qui posent plusieurs défis de recherche abordés dans cette thèse. D'un point de vue technique, les bases de données de céramiques présentent différents formats de fichiers, protocoles d'accès et langages d'interrogation. Du point de vue des données, il existe une grande hétérogénéité et les experts ont différentes façons de représenter et de stocker les données. Il n'existe pas de contenu et de terminologie standard, surtout en ce qui concerne la description des céramiques. De plus, la navigation et l'observation des données sont difficiles. L'intégration des données est également complexe en raison de laprésence de différentes dimensions provenant de bases de données distantes, qui décrivent les mêmes catégories d'objets de manières différentes.En conséquence, ce projet de thèse vise à apporter aux archéologues et aux archéomètres des outils qui leur permettent d'enrichir leurs connaissances en combinant différentes informations sur les céramiques. Nous divisons notre travail en deux parties complémentaires : (1) Modélisation de données archéologiques complexes, et (2) Partitionnement de données (clustering) archéologiques complexes. La première partie de cette thèse est consacrée à la conception d'un modèle de données archéologiques complexes pour le stockage des données céramiques. Cette base de donnée alimente également un entrepôt de données permettant des analyses en ligne (OLAP). La deuxième partie de la thèse est consacrée au clustering (catégorisation) des objets céramiques. Pour ce faire, nous proposons une approche floue, dans laquelle un objet céramique peut appartenir à plus d'un cluster (d'une catégorie). Ce type d'approche convient bien à la collaboration avec des experts, enouvrant de nouvelles discussions basées sur les résultats du clustering.Nous contribuons au clustering flou (fuzzy clustering) au sein de trois sous-tâches : (i) une nouvelle méthode d'initialisation des clusters flous qui maintient linéaire la complexité de l'approche ; (ii) un indice de qualité innovant qui permet de trouver le nombre optimal de clusters ; et (iii) l'approche Multiple Clustering Analysis qui établit des liens intelligents entre les données visuelles, textuelles et numériques, ce qui permet de combiner tous les types d'informations sur les céramiques. Par ailleurs, les méthodes que nous proposons pourraient également être adaptées à d'autres domaines d'application tels que l'économie ou la médecine. / Ceramics are one of the most important archaeological materials to help in the reconstruction of past civilizations. Information about complex ceramic objects is composed of textual, numerical and multimedia data, which induce several research challenges addressed in this thesis. From a technical perspective, ceramic databases have different file formats, access protocols and query languages. From a data perspective, ceramic data are heterogeneous and experts have differentways of representing and storing data. There is no standardized content and terminology, especially in terms of description of ceramics. Moreover, data navigation and observation are difficult. Data integration is also difficult due to the presence of various dimensions from distant databases, which describe the same categories of objects in different ways.Therefore, the research project presented in this thesis aims to provide archaeologists and archaeological scientists with tools for enriching their knowledge by combining different information on ceramics. We divide our work into two complementary parts: (1) Modeling of Complex Archaeological Data and (2) Clustering Analysis of Complex Archaeological Data. The first part of this thesis is dedicated to the design of a complex archaeological database model for the storage of ceramic data. This database is also used to source a data warehouse for doing online analytical processing (OLAP). The second part of the thesis is dedicated to an in-depth clustering (categorization) analysis of ceramic objects. To do this, we propose a fuzzy approach, where ceramic objects may belong to more than one cluster (category). Such a fuzzy approach is well suited for collaborating with experts, by opening new discussions based on clustering results.We contribute to fuzzy clustering in three sub-tasks: (i) a novel fuzzy clustering initialization method that keeps the fuzzy approach linear; (ii) an innovative quality index that allows finding the optimal number of clusters; and (iii) the Multiple Clustering Analysis approach that builds smart links between visual, textual and numerical data, which assists in combining all types ofceramic information. Moreover, the methods we propose could also be adapted to other application domains such as economy or medicine.

Submitted by Lucas Pimentel Vilela (lucaspimentelvilela@gmail.com) on 2017-05-04T01:19:37Z No. of bitstreams: 1 Hypothesis Testing in Econometric Models - Vilela 2017.pdf: 2079231 bytes, checksum: d0387462f36ab4ab7e5d33163bb68416 (MD5) / Approved for entry into archive by Maria Almeida (maria.socorro@fgv.br) on 2017-05-15T19:31:43Z (GMT) No. of bitstreams: 1 Hypothesis Testing in Econometric Models - Vilela 2017.pdf: 2079231 bytes, checksum: d0387462f36ab4ab7e5d33163bb68416 (MD5) / Made available in DSpace on 2017-05-15T19:32:18Z (GMT). No. of bitstreams: 1 Hypothesis Testing in Econometric Models - Vilela 2017.pdf: 2079231 bytes, checksum: d0387462f36ab4ab7e5d33163bb68416 (MD5) Previous issue date: 2015-12-11 / This thesis contains three chapters. The first chapter considers tests of the parameter of an endogenous variable in an instrumental variables regression model. The focus is on one-sided conditional t-tests. Theoretical and numerical work shows that the conditional 2SLS and Fuller t-tests perform well even when instruments are weakly correlated with the endogenous variable. When the population F-statistic is as small as two, the power is reasonably close to the power envelopes for similar and non-similar tests which are invariant to rotation transformations of the instruments. This finding is surprising considering the poor performance of two-sided conditional t-tests found in Andrews, Moreira, and Stock (2007). These tests have bad power because the conditional null distributions of t-statistics are asymmetric when instruments are weak. Taking this asymmetry into account, we propose two-sided tests based on t-statistics. These novel tests are approximately unbiased and can perform as well as the conditional likelihood ratio (CLR) test. The second and third chapters are interested in maxmin and minimax regret tests for broader hypothesis testing problems. In the second chapter, we present maxmin and minimax regret tests satisfying more general restrictions than the alpha-level and the power control over all alternative hypothesis constraints. More general restrictions enable us to eliminate trivial known tests and obtain tests with desirable properties, such as unbiasedness, local unbiasedness and similarity. In sequence, we prove that both tests always exist and under suficient assumptions, they are Bayes tests with priors that are solutions of an optimization problem, the dual problem. In the last part of the second chapter, we consider testing problems that are invariant to some group of transformations. Under the invariance of the hypothesis testing, the Hunt-Stein Theorem proves that the search for maxmin and minimax regret tests can be restricted to invariant tests. We prove that the Hunt-Stein Theorem still holds under the general constraints proposed. In the last chapter we develop a numerical method to implement maxmin and minimax regret tests proposed in the second chapter. The parametric space is discretized in order to obtain testing problems with a finite number of restrictions. We prove that, as the discretization turns finer, the maxmin and the minimax regret tests satisfying the finite number of restrictions have the same alternative power of the maxmin and minimax regret tests satisfying the general constraints. Hence, we can numerically implement tests for a finite number of restrictions as an approximation for the tests satisfying the general constraints. The results in the second and third chapters extend and complement the maxmin and minimax regret literature interested in characterizing and implementing both tests. / Esta tese contém três capítulos. O primeiro capítulo considera testes de hipóteses para o coeficiente de regressão da variável endógena em um modelo de variáveis instrumentais. O foco é em testes-t condicionais para hipóteses unilaterais. Trabalhos teóricos e numéricos mostram que os testes-t condicionais centrados nos estimadores de 2SLS e Fuller performam bem mesmo quando os instrumentos são fracamente correlacionados com a variável endógena. Quando a estatística F populacional é menor que dois, o poder é razoavelmente próximo do poder envoltório para testes que são invariantes a transformações que rotacionam os instrumentos (similares ou não similares). Este resultado é surpreendente considerando a baixa performance dos testes-t condicionais para hipóteses bilaterais apresentado em Andrews, Moreira, and Stock (2007). Estes testes possuem baixo poder porque as distribuições das estatísticas-t na hipótese nula são assimétricas quando os instrumentos são fracos. Explorando tal assimetria, nós propomos testes para hipóteses bilaterais baseados em estatísticas-t. Estes testes são aproximadamente não viesados e podem performar tão bem quanto o teste de razão de máxima verossimilhança condicional. No segundo e no terceiro capítulos, nosso interesse é em testes do tipo maxmin e minimax regret para testes de hipóteses mais gerais. No segundo capítulo, nós apresentamos testes maxmin e minimax regret que satisfazem restrições mais gerais que as restrições de tamanho e de controle sobre todo o poder na hipótese alternativa. Restrições mais gerais nos possibilitam eliminar testes triviais e obter testes com propriedades desejáveis, como por exemplo não viés, não viés local e similaridade. Na sequência, nós provamos que ambos os testes existem e, sob condições suficientes, eles são testes Bayesianos com priors que são solução de um problema de otimização, o problema dual. Na última parte do segundo capítulo, nós consideramos testes de hipóteses que são invariantes à algum grupo de transformações. Sob invariância, o Teorema de Hunt-Stein implica que a busca por testes maxmin e minimax regret pode ser restrita a testes invariantes. Nós provamos que o Teorema de Hunt-Stein continua válido sob as restrições gerais propostas. No último capítulo, nós desenvolvemos um procedimento numérico para implementar os testes maxmin e minimax regret propostos no segundo capítulo. O espaço paramétrico é discretizado com o objetivo de obter testes de hipóteses com um número finito de pontos. Nós provamos que, ao considerarmos partições mais finas, os testes maxmin e minimax regret que satisfazem um número finito de pontos possuem o mesmo poder na hipótese alternativa que os testes maxmin e minimax regret que satisfazem as restrições gerais. Portanto, nós podemos implementar numericamente os testes que satisfazem um número finito de pontos como aproximação aos testes que satisfazem as restrições gerais.