This dissertation addresses the development of enhanced formulations for minimax and mixed-integer programming models for certain industrial and logistical systems, along with the design and implementation of efficient algorithmic strategies. We first examine the general class of minimax mixed-integer 0-1 problems of the type that frequently arise in decomposition approaches and in a variety of location and scheduling problems. We conduct an extensive polyhedral analysis of this problem in order to tighten its representation using the Reformulation-Linearization/Convexification Technique (RLT), and demonstrate the benefits of the resulting lifted formulations for several classes of problems. Specifically, we investigate RLT-enhanced Lagrangian dual formulations for the class of minimax mixed-integer 0-1 problems in concert with deflected/conjugate subgradient algorithms. In addition, we propose two general purpose lifting mechanisms for tightening the mathematical programming formulations associated with such minimax optimization problems. Next, we explore novel continuous nonconvex as well as lifted discrete formulations for the notoriously challenging class of job-shop scheduling problems with the objective of minimizing the maximum completion time (i.e., minimizing the makespan). In particular, we develop an RLT-enhanced continuous nonconvex model for the job-shop problem based on a quadratic formulation of the job sequencing constraints on machines. The tight linear programming relaxation that is induced by this formulation is then embedded in a globally convergent branch-and-bound algorithm. Furthermore, we design another novel formulation for the job-shop scheduling problem that possesses a tight continuous relaxation, where the non-overlapping job sequencing constraints on machines are modeled via a lifted asymmetric traveling salesman problem (ATSP) construct, and specific sets of valid inequalities and RLT-based enhancements are incorporated to further tighten the resulting mathematical program. The efficacy of our enhanced models is demonstrated by an extensive computational experiment using classical benchmark problems from the literature. Our results reveal that the LP relaxations produced by the lifted ATSP-based models provide very tight lower bounds, and directly yield a 0\% optimality gap for many benchmark problems, thereby substantially dominating other alternative mixed-integer programming models available for this class of problems. Notably, our lifted ATSP-based formulation produced a 0\% optimality gap via the root node LP relaxation for 50\% of the classical problem instances due to Lawrence. We also investigate enhanced model formulations and specialized, efficient solution methodologies for applications arising in four particular industrial and sports scheduling settings. The first of these was posed to us by a major trucking company (Volvo Logistics North America), and concerns an integrated assembly and routing problem, which is a unique study of its kind in the literature. In this context, we examine the general class of logistical systems where it is desirable to appropriately ascertain the joint composition of the sequences of vehicles that are to be physically connected along with determining their delivery routes. Such assembly-routing problems occur in the truck manufacturing industry where different models of vehicles designed for a network of customers need to be composed into compatible groups (assemblies) and subsequently dispatched via appropriately optimized delivery routes that are restricted by the particular sequence in which the trucks are connected. A similar structure is exhibited in the business of shipping goods via boat-towed barges along inland waterways, or via trains through railroad networks. We present a novel modeling framework and column generation-based optimization approach for this challenging class of joint vehicle assembly-routing problems. In addition, we suggest several extensions to accommodate particular industrial restrictions where assembly sequence-dependent delivery routes are necessary, as well as those where limited driver- and equipment-related resources are available. Computational experience is provided using large-scale realistic data to demonstrate the applicability of our suggested methodology in practice. The second application addressed pertains to a production planning problem faced by a major motorcycle manufacturing firm (Harley-Davidson Motor Company). We consider the problem of partitioning and sequencing the production of different manufactured items in mixed-model assembly lines, where each model has various specific options and designated destinations. We propose a mixed-integer programming formulation (MPSP1) for this problem that sequences the manufactured goods within production batches in order to balance the motorcycle model and destination outputs as well as the load demands on material and labor resources. An alternative (relaxed) formulation (MPSP2) is also presented to model a closely related case where all production decisions and outputs are monitored within a common sequence of batches, which permits an enhanced tighter representation via an additional set of hierarchical symmetry-defeating constraints that impart specific identities amongst batches of products under composition. The latter model inspires a third set partitioning-based formulation in concert with an efficient column generation approach that directly achieves the joint partitioning of jobs into batches along with ascertaining the sequence of jobs within each composed batch. Finally, we investigate a subgradient-based optimization strategy that exploits a non-differentiable optimization formulation, which is prompted by the flexibility in the production process as reflected in the model via several soft-constraints, thereby providing a real-time decision-making tool. Computational experience is presented to demonstrate the relative effectiveness of the different proposed formulations and the associated optimization strategies for solving a set of realistic problem instances. The third application pertains to the problem of matching or assigning subassembly parts in assembly lines, where we seek to minimize the total deviation of the resulting final assemblies from a vector of nominal and mean quality characteristic values. We introduce three symmetry-defeating enhancements for an existing assignment-based model, and highlight the critical importance of using particular types of symmetry-defeating hierarchical constraints that preserve the model structure. We also develop an alternative set partitioning-based formulation in concert with a column generation approach that efficiently exploits the structure of the problem. A special complementary column generation feature is proposed, and we provide insights into its vital role for the proposed column generation strategy, as well as highlight its benefits in the broader context of set partitioning-based formulations that are characterized by columns having relatively dense non-zero values. In addition, we develop several heuristic procedures. Computational experience is presented to demonstrate the relative effectiveness of the different adopted strategies for solving a set of realistic problem instances. Finally, we analyze a doubles tennis scheduling problem in the context of a training tournament as prompted by a tennis club in Virginia, and develop two alternative 0-1 mixed-integer programming models, each with three different objective functions that attempt to balance the partnership and the opponentship pairings among the players. Our analysis and computational experience demonstrate the superiority of one of these models over the other, and reflect the importance of model structure in formulating discrete optimization problems. Furthermore, we design effective symmetry-defeating strategies that impose certain decision hierarchies within the models, which serve to significantly enhance algorithmic performance. In particular, our study provides the insight that the special structure of the mathematical program to which specific tailored symmetry-defeating constraints are appended can greatly influence their pruning effect. We also propose a novel nonpreemptive multi-objective programming strategy in concert with decision hierarchies, and highlight its effectiveness and conceptual value in enhancing problem solvability. Finally, four specialized heuristics are devised and are computationally evaluated along with the exact solution schemes using a set of realistic practical test problems. Aside from the development of specialized effective models and algorithms for particular interesting and challenging applications arising in different assembly, routing, and scheduling contexts, this dissertation makes several broader contributions that emerge from the foregoing studies, which are generally applicable to solving formidable combinatorial optimization problems. First, we have shown that it is of utmost importance to enforce symmetry-defeating constraints that preserve the structure of mathematical programs to which they are adjoined, so that their pruning effects are most efficiently coupled with the branch-and-bound strategies that are orchestrated within mathematical programming software packages. In addition, our work provides the insight that the concept of symmetry compatible formulations plays a crucial role in the effectiveness of implementing any particular symmetry-defeating constraints. In essence, if the root node LP solution of the original formulation does not conform relatively well with the proposed symmetry-defeating hierarchical constraints, then a significant branching effort might be required to identify a good solution that is compatible with the pattern induced by the selected symmetry-defeating constraints. Therefore, it is advisable to enforce decision hierarchies that conform as much as possible with the problem structure as well as with the initial LP relaxation. Second, we have introduced an alternative concept for defeating symmetry via augmented objective functions. This concept prompts the incorporation of objective perturbation terms that discriminate amongst subsets of originally undistinguishable solution structures and, in particular, leads to the development of a nonpreemptive multiobjective programming approach based on, and combined with, symmetry-defeating constraints. Interestingly, nonpreemptive multiobjective programming approaches that accommodate symmetry-defeating hierarchical objective terms induce a root node solution that is compatible with the imposed symmetry-defeating constraints, and hence affords an automated alternative to the aforementioned concept of symmetry compatible formulations. Third, we have proposed a new idea of complementary column generation in the context of column generation approaches that generally provide a versatile framework for analyzing industrial-related, integrated problems that involve the joint optimization of multiple operational decisions, such as assembly and routing, or partitioning and scheduling. In such situations, we have reinforced the insight that assignment-related problems that involve collections of objects (production batches, final assemblies, etc.) whose permutation yields equivalent symmetric solutions may be judiciously formulated as set partitioning models. The latter can then be effectively tackled via column generation approaches, thereby implicitly obviating the foregoing combinatorial symmetric reflections through the dynamic generation of attractive patterns or columns. The complementary column generation feature we have proposed and investigated in this dissertation proves to be particularly valuable for such set partitioning formulations that involve columns having relatively dense non-zero values. The incorporation of this feature guarantees that every LP iteration (involving the solution of a restricted master program and its associated subproblem) systematically produces a consistent set of columns that collectively qualify as a feasible solution to the problem under consideration. Upon solving the problem to optimality as a linear program, the resultant formulation encompasses multiple feasible solutions that generally include optimal or near-optimal solutions to the original integer-restricted set partitioning formulation, thereby yielding a useful representation for designing heuristic methods as well as exact branch-and-price algorithms. In addition, using duality theory and considering set partitioning problems where the number of patterns needed to collectively compose a feasible solution is bounded, we have derived a lower bound on the objective value that is updated at every LP phase iteration. By virtue of this sequence of lower bounds and the availability of upper bounds via the restricted master program at every LP phase iteration, the LP relaxation of the set partitioning problem is efficiently solved as using a pre-specified optimality tolerance. This yields enhanced algorithmic performance due to early termination strategies that successfully mitigate the tailing-off effect that is commonly witnessed for simplex-based column generation approaches. / Ph. D.

À partir des observations Z(n) = {(Xi, Yi), i = 1, ..., n} satisfaisant Yi = f(Xi) + ζi, nous voulons reconstruire la fonction f. Nous évaluons la qualité d'estimation par deux critères : le risque Ls et le risque uniforme. Dans ces deux cas, les hypothèses imposées sur la distribution du bruit ζi serons de moment borné et de type sous-gaussien respectivement. En proposant une collection des estimateurs à noyau, nous construisons une procédure, qui est initié par Goldenshluger et Lepski, pour choisir l'estimateur dans cette collection, sans aucune condition sur f. Nous prouvons ensuite que cet estimateur satisfait une inégalité d'oracle, qui nous permet d'obtenir les estimations minimax et minimax adaptatives sur les classes de Hölder anisotropes. / From the observation Z(n) = {(Xi, Yi), i = 1, ..., n} satisfying Yi = f(Xi) + ζi, we would like to approximate the function f. This problem will be considered in two cases of loss function, Ls-risk and uniform risk, where the condition imposed on the distribution of the noise ζi is of bounded moment and of type sub-gaussian, respectively. From a proposed family of kernel estimators, we construct a procedure, which is initialized by Goldenshluger and Lepski, to choose in this family a final estimator, with no any assumption imposed on f. Then, we show that this estimator satisfies an oracle inequality which implies the minimax and minimax adaptive estimation over the anisotropic Hölder classes.

Les travaux présentés dans ce mémoire contribuent à la définition de méthodes pour la détection et le diagnostic de défauts affectant les systèmes aéronautiques. Un système représentatif sert de support d'étude, constitué du modèle non linéaire à six degrés de liberté d'un missile intercepteur, de ses capteurs et actionneurs ainsi que d'une boucle de guidage-pilotage. La première partie est consacrée au développement de deux méthodes de diagnostic exploitant l'information de commande en boucle fermée et les caractéristiques des modèles aéronautiques. La première méthode utilise les objectifs de commande induits par les lois de guidage-pilotage pour générer des résidus indiquant la présence de défauts. Ceci permet la détection des défauts sur les actionneurs et les capteurs, ainsi que leur localisation pour ces derniers. La deuxième méthode exploite la mesure de dérivées des variables d'état (via une centrale inertielle) pour estimer la valeur de la commande réalisée par les actionneurs, sans intégration du modèle non linéaire du système. Le diagnostic est alors effectué en comparant cette estimée avec la valeur désirée, ce qui permet la détection, la localisation et l'identification de défauts multiples sur les actionneurs.La seconde partie propose une méthodologie de réglage automatique des paramètres internes (les hyperparamètres) de méthodes de diagnostic. Ceci permet une comparaison plus objective entre les méthodes en évaluant la meilleure performance de chacune. Le réglage est vu comme un problème d'optimisation globale, la fonction à optimiser étant calculée via la simulation numérique (potentiellement coûteuse) de cas test. La méthodologie proposée est fondée sur un métamodèle de krigeage et une procédure itérative d’optimisation bayésienne, qui permettent d’aborder ce problème à faible coût de calcul. Un nouvel algorithme est proposé afin d'optimiser les hyperparamètres d'une façon robuste vis à vis de la variabilité des cas test pertinents.Mots clés : détection et diagnostic de défauts, guidage-pilotage, krigeage, minimax continu, optimisation globale, redondance analytique, réglage automatique, systèmes aéronautiques. / This manuscript reports contributions to the development of methods for fault detection and diagnosis applied to aeronautical systems. A representative system is considered, composed of the six-degree-of-freedom nonlinear model of a surface-to-air missile, its sensors, actuators and the associated GNC scheme. The first part is devoted to the development of two fault diagnosis approaches that take advantage of closed-loop control information, along with the characteristics of aeronautical models. The first method uses control objectives resulting from guidance laws to generate residuals indicative of the presence of faults. This enables the detection of both actuator and sensor faults, and the isolation of sensor faults. The second method exploits the measurement of derivatives of state variables (as provided by an IMU) to estimate the control input as achieved by actuators, without the need to integrate the nonlinear model. Detection, isolation and identification of actuator faults can then be performed by comparing this estimate with the desired control input.The second part presents a new automatic-tuning methodology for the internal parameters (the hyperparameters) of fault diagnosis methods. This allows a fair comparison between methods by evaluating their best performance. Tuning is formalised as the global optimization of a black-box function that is obtained through the (costly) numerical simulation of a set of test cases. The methodology proposed here is based on Kriging and Bayesian optimization, which make it possible to tackle this problem at a very reduced computational cost. A new algorithm is developed to address the optimization of hyperparameters in a way that is robust to the variability of the test cases of interest.

Sei (X(t), t>= -r) ein stationärer stochastischer Prozess, der die affine stochastische Differentialgleichung mit Gedächtnis dX(t)=L(X(t+s))dt+sigma dW(t), t>= 0, löst, wobei sigma>0, (W(t), t>=0) eine Standard-Brownsche Bewegung und L ein stetiges lineares Funktional auf dem Raum der stetigen Funktionen auf [-r,0], dargestellt durch ein endliches signiertes Maß a, bezeichnet. Wir nehmen an, dass eine Trajektorie (X(t), -r 0, konvergiert. Diese Rate ist schlechter als in vielen klassischen Fällen. Wir beweisen jedoch eine untere Schranke, die zeigt, dass keine Schätzung eine bessere Rate im Minimax-Sinn aufweisen kann. Für zeit-diskrete Beobachtungen von maximalem Abstand Delta konvergiert die Galerkin-Schätzung immer noch mit obiger Rate, sofern Delta is in etwa von der Ordnung T^(-1/2). Hingegen wird bewiesen, dass für festes Delta unabhängig von T die Rate sich signifikant verschlechtern muss, indem eine untere Schranke von T^(-s/(2s+6)) gezeigt wird. Außerdem wird eine adaptive Schätzung basierend auf Wavelet-Thresholding-Techniken für das assoziierte schlechtgestellte Problem konstruiert. Diese nichtlineare Schätzung erreicht die obige Minimax-Rate sogar für die allgemeinere Klasse der Besovräume B^s_(p,infinity) mit p>max(6/(2s+3),1). Die Restriktion p>=max(6/(2s+3),1) muss für jede Schätzung gelten und ist damit inhärent mit dem Schätzproblem verknüpft. Schließlich wird ein Hypothesentest mit nichtparametrischer Alternative vorgestellt, der zum Beispiel für das Testen auf Gedächtnis verwendet werden kann. Dieser Test ist anwendbar für eine L^2-Trennungsrate zwischen Hypothese und Alternative der Ordnung T^(-s/(2s+2.5)). Diese Rate ist wiederum beweisbar optimal für jede mögliche Teststatistik. Für die Beweise müssen die Parameterabhängigkeit der stationären Lösungen sowie die Abbildungseigenschaften der assoziierten Kovarianzoperatoren detailliert bestimmt werden. Weitere Resultate von allgemeinem Interessen beziehen sich auf die Mischungseigenschaft der stationären Lösung, eine Fallstudie zu exponentiellen Gewichtsfunktionen sowie der Approximation des stationären Prozesses durch autoregressive Prozesse in diskreter Zeit. / Let (X(t), t>= -r) be a stationary stochastic process solving the affine stochastic delay differential equation dX(t)=L(X(t+s))dt+sigma dW(t), t>= 0, with sigma>0, (W(t), t>=0) a standard one-dimensional Brownian motion and with a continuous linear functional L on the space of continuous functions on [-r,0], represented by a finite signed measure a. Assume that a trajectory (X(t), -r 0. This rate is worse than those obtained in many classical cases. However, we prove a lower bound, stating that no estimator can attain a better rate of convergence in a minimax sense. For discrete time observations of maximal distance Delta, the Galerkin estimator still attains the above asymptotic rate if Delta is roughly of order T^(-1/2). In contrast, we prove that for observation intervals Delta, with Delta independent of T, the rate must deteriorate significantly by providing the rate estimate T^(-s/(2s+6)) from below. Furthermore, we construct an adaptive estimator by applying wavelet thresholding techniques to the corresponding ill-posed inverse problem. This nonlinear estimator attains the above minimax rate even for more general classes of Besov spaces B^s_(p,infinity) with p>max(6/(2s+3),1). The restriction p >= 6/(2s+3) is shown to hold for any estimator, hence to be inherently associated with the estimation problem. Finally, a hypothesis test with a nonparametric alternative is constructed that could for instance serve to decide whether a trajectory has been generated by a stationary process with or without time delay. The test works for an L^2-separation rate between hypothesis and alternative of order T^(-s/(2s+2.5)). This rate is again shown to be optimal among all conceivable tests. For the proofs, the parameter dependence of the stationary solutions has to be studied in detail and the mapping properties of the associated covariance operators have to be determined exactly. Other results of general interest concern the mixing properties of the stationary solution, a case study for exponential weight functions and the approximation of the stationary process by discrete time autoregressive processes.

Die Schätzung von Quantilen und verwandten Funktionalen wird in zwei inversen Problemen behandelt: dem klassischen Dekonvolutionsmodell sowie dem Lévy-Modell in dem ein Lévy-Prozess beobachtet wird und Funktionale des Sprungmaßes geschätzt werden. Im einem abstrakteren Rahmen wird semiparametrische Effizienz im Sinne von Hájek-Le Cam für Funktionalschätzung in regulären, inversen Modellen untersucht. Ein allgemeiner Faltungssatz wird bewiesen, der auf eine große Klasse von statistischen inversen Problem anwendbar ist. Im Dekonvolutionsmodell beweisen wir, dass die Plugin-Schätzer der Verteilungsfunktion und der Quantile effizient sind. Auf der Grundlage von niederfrequenten diskreten Beobachtungen des Lévy-Prozesses wird im nichtlinearen Lévy-Modell eine Informationsschranke für die Schätzung von Funktionalen des Sprungmaßes hergeleitet. Die enge Verbindung zwischen dem Dekonvolutionsmodell und dem Lévy-Modell wird präzise beschrieben. Quantilschätzung für Dekonvolutionsprobleme wird umfassend untersucht. Insbesondere wird der realistischere Fall von unbekannten Fehlerverteilungen behandelt. Wir zeigen unter minimalen und natürlichen Bedingungen, dass die Plugin-Methode minimax optimal ist. Eine datengetriebene Bandweitenwahl erlaubt eine optimale adaptive Schätzung. Quantile werden auf den Fall von Lévy-Maßen, die nicht notwendiger Weise endlich sind, verallgemeinert. Mittels äquidistanten, diskreten Beobachtungen des Prozesses werden nichtparametrische Schätzer der verallgemeinerten Quantile konstruiert und minimax optimale Konvergenzraten hergeleitet. Als motivierendes Beispiel von inversen Problemen untersuchen wir ein Finanzmodell empirisch, in dem ein Anlagengegenstand durch einen exponentiellen Lévy-Prozess dargestellt wird. Die Quantilschätzer werden auf dieses Modell übertragen und eine optimale adaptive Bandweitenwahl wird konstruiert. Die Schätzmethode wird schließlich auf reale Daten von DAX-Optionen angewendet. / The estimation of quantiles and realated functionals is studied in two inverse problems: the classical deconvolution model and the Lévy model, where a Lévy process is observed and where we aim for the estimation of functionals of the jump measure. From a more abstract perspective we study semiparametric efficiency in the sense of Hájek-Le Cam for functional estimation in regular indirect models. A general convolution theorem is proved which applies to a large class of statistical inverse problems. In particular, we consider the deconvolution model, where we prove that our plug-in estimators of the distribution function and of the quantiles are efficient. In the nonlinear Lévy model based on low-frequent discrete observations of the Lévy process, we deduce an information bound for the estimation of functionals of the jump measure. The strong relationship between the Lévy model and the deconvolution model is given a precise meaning. Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Under minimal and natural conditions we show that the plug-in method is minimax optimal. A data-driven bandwidth choice yields optimal adaptive estimation. The concept of quantiles is generalized to the possibly infinite Lévy measures by considering left and right tail integrals. Based on equidistant discrete observations of the process, we construct a nonparametric estimator of the generalized quantiles and derive minimax convergence rates. As a motivating financial example for inverse problems, we empirically study the calibration of an exponential Lévy model for asset prices. The estimators of the generalized quantiles are adapted to this model. We construct an optimal adaptive quantile estimator and apply the procedure to real data of DAX-options.

Cette thèse travaille principalement sur trois sujets. Le premier concentre sur le clustering en ligne dans lequel nous présentons un nouvel algorithme stochastique adaptatif pour regrouper des ensembles de données en ligne. Cet algorithme repose sur l'approche quasi-bayésienne, avec une estimation dynamique (i.e., dépendant du temps) du nombre de clusters. Nous prouvons que cet algorithme atteint une borne de regret de l'ordre et que cette borne est asymptotiquement minimax sous la contrainte sur le nombre de clusters. Nous proposons aussi une implémentation par RJMCMC. Le deuxième sujet est lié à l'apprentissage séquentiel des courbes principales qui cherche à résumer une séquence des données par une courbe continue. Pour ce faire, nous présentons une procédure basée sur une approche maximum a posteriori pour le quasi-posteriori de Gibbs. Nous montrons que la borne de regret de cet algorithme et celui de sa version adaptative est sous-linéaire en l'horizon temporel T. En outre, nous proposons une implémentation par un algorithme glouton local qui intègre des éléments de sleeping experts et de bandit à plusieurs bras. Le troisième concerne les travaux qui visent à accomplir des tâches pratiques au sein d'iAdvize, l'entreprise qui soutient cette thèse. Il inclut l'analyse des sentiments pour les messages textuels et l'implémentation de chatbot dans lesquels la première est réalisé par les méthodes classiques dans la fouille de textes et les statistiques et la seconde repose sur le traitement du langage naturel et les réseaux de neurones artificiels. / This thesis works mainly on three subjects. The first one is online clustering in which we introduce a new and adaptive stochastic algorithm to cluster online dataset. It relies on a quasi-Bayesian approach, with a dynamic (i.e., time-dependent) estimation of the (unknown and changing) number of clusters. We prove that this algorithm has a regret bound of the order of and is asymptotically minimax under the constraint on the number of clusters. A RJMCMC-flavored implementation is also proposed. The second subject is related to the sequential learning of principal curves which seeks to represent a sequence of data by a continuous polygonal curve. To this aim, we introduce a procedure based on the MAP of Gibbs-posterior that can give polygonal lines whose number of segments can be chosen automatically. We also show that our procedure is supported by regret bounds with sublinear remainder terms. In addition, a greedy local search implementation that incorporates both sleeping experts and multi-armed bandit ingredients is presented. The third one concerns about the work which aims to fulfilling practical tasks within iAdvize, the company which supports this thesis. It includes sentiment analysis for textual messages by using methods in both text mining and statistics, and implementation of chatbot based on nature language processing and neural networks.

La simulation numérique est devenue une alternative à l’expérimentation réelle pour étudier des phénomènes physiques. Cependant, les phénomènes complexes requièrent en général un nombre important de simulations, chaque simulation étant très coûteuse en temps de calcul. Une approche basée sur la théorie des plans d’expériences est souvent utilisée en vue de réduire ce coût de calcul. Elle consiste à partir d’un nombre réduit de simulations, organisées selon un plan d’expériences numériques, à construire un modèle d’approximation souvent appelé métamodèle, alors beaucoup plus rapide à évaluer que le code lui-même. Traditionnellement, les plans utilisés sont des plans de type Space-Filling Design (SFD). La première partie de la thèse concerne la construction de plans d’expériences SFD à taille fixe adaptés à l’identification d’un modèle de krigeage car le krigeage est un des métamodèles les plus populaires. Nous étudions l’impact de la contrainte Hypercube Latin (qui est le type de plans les plus utilisés en pratique avec le modèle de krigeage) sur des plans maximin-optimaux. Nous montrons que cette contrainte largement utilisée en pratique est bénéfique quand le nombre de points est peu élevé car elle atténue les défauts de la configuration maximin-optimal (majorité des points du plan aux bords du domaine). Un critère d’uniformité appelé discrépance radiale est proposé dans le but d’étudier l’uniformité des points selon leur position par rapport aux bords du domaine. Ensuite, nous introduisons un proxy pour le plan minimax-optimal qui est le plan le plus proche du plan IMSE (plan adapté à la prédiction par krigeage) et qui est coûteux en temps de calcul, ce proxy est basé sur les plans maximin-optimaux. Enfin, nous présentons une procédure bien réglée de l’optimisation par recuit simulé pour trouver les plans maximin-optimaux. Il s’agit ici de réduire au plus la probabilité de tomber dans un optimum local. La deuxième partie de la thèse porte sur un problème légèrement différent. Si un plan est construit de sorte à être SFD pour N points, il n’y a aucune garantie qu’un sous-plan à n points (n 6 N) soit SFD. Or en pratique le plan peut être arrêté avant sa réalisation complète. La deuxième partie est donc dédiée au développement de méthodes de planification séquentielle pour bâtir un ensemble d’expériences de type SFD pour tout n compris entre 1 et N qui soient toutes adaptées à la prédiction par krigeage. Nous proposons une méthode pour générer des plans séquentiellement ou encore emboités (l’un est inclus dans l’autre) basée sur des critères d’information, notamment le critère d’Information Mutuelle qui mesure la réduction de l’incertitude de la prédiction en tout point du domaine entre avant et après l’observation de la réponse aux points du plan. Cette approche assure la qualité des plans obtenus pour toutes les valeurs de n, 1 6 n 6 N. La difficulté est le calcul du critère et notamment la génération de plans en grande dimension. Pour pallier ce problème une solution a été présentée. Cette solution propose une implémentation astucieuse de la méthode basée sur le découpage par blocs des matrices de covariances ce qui la rend numériquement efficace. / In recent years, computer simulation models are increasingly used to study complex phenomena. Such problems usually rely on very large sophisticated simulation codes that are very expensive in computing time. The exploitation of these codes becomes a problem, especially when the objective requires a significant number of evaluations of the code. In practice, the code is replaced by global approximation models, often called metamodels, most commonly a Gaussian Process (kriging) adjusted to a design of experiments, i.e. on observations of the model output obtained on a small number of simulations. Space-Filling-Designs which have the design points evenly spread over the entire feasible input region, are the most used designs. This thesis consists of two parts. The main focus of both parts is on construction of designs of experiments that are adapted to kriging, which is one of the most popular metamodels. Part I considers the construction of space-fillingdesigns of fixed size which are adapted to kriging prediction. This part was started by studying the effect of Latin Hypercube constraint (the most used design in practice with the kriging) on maximin-optimal designs. This study shows that when the design has a small number of points, the addition of the Latin Hypercube constraint will be useful because it mitigates the drawbacks of maximin-optimal configurations (the position of the majority of points at the boundary of the input space). Following this study, an uniformity criterion called Radial discrepancy has been proposed in order to measure the uniformity of the points of the design according to their distance to the boundary of the input space. Then we show that the minimax-optimal design is the closest design to IMSE design (design which is adapted to prediction by kriging) but is also very difficult to evaluate. We then introduce a proxy for the minimax-optimal design based on the maximin-optimal design. Finally, we present an optimised implementation of the simulated annealing algorithm in order to find maximin-optimal designs. Our aim here is to minimize the probability of falling in a local minimum configuration of the simulated annealing. The second part of the thesis concerns a slightly different problem. If XN is space-filling-design of N points, there is no guarantee that any n points of XN (1 6 n 6 N) constitute a space-filling-design. In practice, however, we may have to stop the simulations before the full realization of design. The aim of this part is therefore to propose a new methodology to construct sequential of space-filling-designs (nested designs) of experiments Xn for any n between 1 and N that are all adapted to kriging prediction. We introduce a method to generate nested designs based on information criteria, particularly the Mutual Information criterion. This method ensures a good quality forall the designs generated, 1 6 n 6 N. A key difficulty of this method is that the time needed to generate a MI-sequential design in the highdimension case is very larg. To address this issue a particular implementation, which calculates the determinant of a given matrix by partitioning it into blocks. This implementation allows a significant reduction of the computational cost of MI-sequential designs, has been proposed.

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L’objectif principal de cette thèse est de développer des méthodologies statistiques adaptées au traitement de données issues de processus stochastiques et plus précisément de processus de Cox.Les problématiques étudiées dans cette thèse sont issues des trois domaines statistiques suivants : les tests non paramétriques, l’estimation non paramétrique à noyaux et l’estimation minimax.Dans un premier temps, nous proposons, dans un cadre fonctionnel, des statistiques de test pour détecter la nature Poissonienne d’un processus de Cox.Nous étudions ensuite le problème de l’estimation minimax de la régression sur un processus de Poisson ponctuel. En se basant sur la décomposition en chaos d’Itô, nous obtenons des vitesses comparables à celles atteintes pour le cas de la régression Lipschitz en dimension finie.Enfin, dans le dernier chapitre de cette thèse, nous présentons un estimateur non-paramétrique de l’intensité d’un processus de Cox lorsque celle-ci est une fonction déterministe d’un co-processus. / The main purpose of this thesis is to develop statistical methodologies for stochastic processes data and more precisely Cox process data.The problems considered arise from three different contexts: nonparametric tests, nonparametric kernel estimation and minimax estimation.We first study the statistical test problem of detecting wether a Cox process is Poisson or not.Then, we introduce a semiparametric estimate of the regression over a Poisson point process. Using Itô’s famous chaos expansion for Poisson functionals, we derive asymptotic minimax properties of our estimator.Finally, we introduce a nonparametric estimate of the intensity of a Cox process whenever it is a deterministic function of a known coprocess.