La première partie de cette thèse concerne l'inférence de modèles statistiques non normalisés. Nous étudions deux méthodes d'inférence basées sur de l'échantillonnage aléatoire : Monte-Carlo MLE (Geyer, 1994), et Noise Contrastive Estimation (Gutmann et Hyvarinen, 2010). Cette dernière méthode fut soutenue par une justification numérique d'une meilleure stabilité, mais aucun résultat théorique n'avait encore été prouvé. Nous prouvons que Noise Contrastive Estimation est plus robuste au choix de la distribution d'échantillonnage. Nous évaluons le gain de précision en fonction du budget computationnel. La deuxième partie de cette thèse concerne l'échantillonnage aléatoire approché pour les distributions de grande dimension. La performance de la plupart des méthodes d’échantillonnage se détériore rapidement lorsque la dimension augmente, mais plusieurs méthodes ont prouvé leur efficacité (e.g. Hamiltonian Monte Carlo, Langevin Monte Carlo). Dans la continuité de certains travaux récents (Eberle et al., 2017 ; Cheng et al., 2018), nous étudions certaines discrétisations d’un processus connu sous le nom de kinetic Langevin diffusion. Nous établissons des vitesses de convergence explicites vers la distribution d'échantillonnage, qui ont une dépendance polynomiale en la dimension. Notre travail améliore et étend les résultats de Cheng et al. pour les densités log-concaves. / The first part of this thesis concerns the inference of un-normalized statistical models. We study two methods of inference based on sampling, known as Monte-Carlo MLE (Geyer, 1994), and Noise Contrastive Estimation (Gutmann and Hyvarinen, 2010). The latter method was supported by numerical evidence of improved stability, but no theoretical results had yet been proven. We prove that Noise Contrastive Estimation is more robust to the choice of the sampling distribution. We assess the gain of accuracy depending on the computational budget. The second part of this thesis concerns approximate sampling for high dimensional distributions. The performance of most samplers deteriorates fast when the dimension increases, but several methods have proven their effectiveness (e.g. Hamiltonian Monte Carlo, Langevin Monte Carlo). In the continuity of some recent works (Eberle et al., 2017; Cheng et al., 2018), we study some discretizations of the kinetic Langevin diffusion process and establish explicit rates of convergence towards the sampling distribution, that scales polynomially fast when the dimension increases. Our work improves and extends the results established by Cheng et al. for log-concave densities.

Η παρούσα μεταπτυχιακή διατριβή εντάσσεται ερευνητικά στην περιοχή της Στατιστικής Θεωρίας Αποφάσεων και ειδικότερα στην εκτίμηση των παραμέτρων στο μοντέλο της διπαραμετρικής εκθετικής κατανομής με παράμετρο θέσης μ και παράμετρο κλίμακος σ. Θεωρούμε το πρόβλημα εκτίμησης των παραμέτρων κλίμακας μ και θέσης σ, όταν μ≤c, όπου c είναι μία γνωστή σταθερά. Αποδεικνύουμε ότι σε σχέση με το κριτήριο του Μέσου Τετραγωνικού Σφάλματος (ΜΤΣ), οι βέλτιστοι αναλλοίωτοι εκτιμητές των μ και σ, είναι μη αποδεκτοί όταν μ≤c, και προτείνουμε βελτιωμένους. Επίσης συγκρίνουμε του εκτιμητές αυτούς σε σχέση με το κριτήριο του Pitman. Επιπλέον, προτείνουμε εκτιμητές που είναι καλύτεροι από τους βέλτιστους αναλλοίωτους εκτιμητές, όταν μ≤c, ως προς την συνάρτηση ζημίας LINEX. Τέλος, η θεωρία που αναπτύσσεται εφαρμόζεται σε δύο ανεξάρτητα δείγματα προερχόμενα από εκθετική κατανομή. / The present master thesis deals with the estimation of the location parameter μ and the scale parameter σ of the two-parameter exponential distribution. We consider the problem of estimation of locasion parameter μ and the scale parameter σ, when it is known apriori that μ≤c, where c is a known constant. We establish that with respect to the mean square error (mse) criterion the best affine estimators of μ and σ in the absence of information μ≤c are inadmissible and we propose estimators which are better than these estimators. Also, we compare these estimators with respect to the Pitman Nearness criterion. We propose estimators which are better than the standard estimators in the unrestricted case with respect to the suitable choise of LINEX loss. Finally, the theory developed is applied to the problem of estimating the location and scale parameters of two exponential distributions when the location parameters are ordered.

Dans ce mémoire, nous étudions le problème de l'estimation de la variance pour les estimateurs par double dilatation et de calage pour l'échantillonnage à deux phases. Nous proposons d'utiliser une décomposition de la variance différente de celle habituellement utilisée dans l'échantillonnage à deux phases, ce qui mène à un estimateur de la variance simplifié. Nous étudions les conditions sous lesquelles les estimateurs simplifiés de la variance sont valides. Pour ce faire, nous considérons les cas particuliers suivants : (1) plan de Poisson à la deuxième phase, (2) plan à deux degrés, (3) plan aléatoire simple sans remise aux deux phases, (4) plan aléatoire simple sans remise à la deuxième phase. Nous montrons qu'une condition cruciale pour la validité des estimateurs simplifiés sous les plans (1) et (2) consiste à ce que la fraction de sondage utilisée pour la première phase soit négligeable (ou petite). Nous montrons sous les plans (3) et (4) que, pour certains estimateurs de calage, l'estimateur simplifié de la variance est valide lorsque la fraction de sondage à la première phase est petite en autant que la taille échantillonnale soit suffisamment grande. De plus, nous montrons que les estimateurs simplifiés de la variance peuvent être obtenus de manière alternative en utilisant l'approche renversée (Fay, 1991 et Shao et Steel, 1999). Finalement, nous effectuons des études par simulation dans le but d'appuyer les résultats théoriques. / In this thesis we study the problem of variance estimation for the double expansion estimator and the calibration estimators in the case of two-phase designs. We suggest to use a variance decomposition different from the one usually used in two-phase sampling, which leads to a simplified variance estimator. We look for the necessary conditions for the simplified variance estimators to be appropriate. In order to do so, we consider the following particular cases : (1) Poisson design at the second phase, (2) two-stage design, (3) simple random sampling at each phase, (4) simple random sampling at the second phase. We show that a crucial condition for the simplified variance estimator to be valid in cases (1) and (2) is that the first phase sampling fraction must be negligible (or small). We also show in cases (3) and (4) that the simplified variance estimator can be used with some calibration estimators when the first phase sampling fraction is negligible and the population size is large enough. Furthermore, we show that the simplified estimators can be obtained in an alternative way using the reversed approach (Fay, 1991 and Shao and Steel, 1999). Finally, we conduct some simulation studies in order to validate the theoretical results.

Nesta tese, desenvolvemos refinamentos assintóticos em modelos lineares generalizados heteroscedásticos (Smyth, 1989). Inicialmente, obtemos a matriz de covariâncias de segunda ordem dos estimadores de máxima verossimilhança corrigidos pelos viés de primeira ordem. Com base na matriz obtida, sugerimos modificações na estatística de Wald. Posteriormente, derivamos os coeficientes do fator de correção tipo-Bartlett para a estatística do teste gradiente. Em seguida, obtemos o coeficiente de assimetria assintótico da distribuição dos estimadores de máxima verossimilhança dos parâmetros do modelo. Finalmente, exibimos o coeficiente de curtose assintótico da distribuição dos estimadores de máxima verossimilhança dos parâmetros do modelo. Analisamos os resultados obtidos através de estudos de simulação de Monte Carlo. / In this thesis, we have developed asymptotic refinements in heteroskedastic generalized linear models (Smyth, 1989). Initially, we obtain the second-order covariance matrix for the maximum likelihood estimators corrected by the bias of first-order. Based on the obtained matrix, we suggest changes in Wald statistics. In addition, we derive the coeficients of the Bartlett-type correction factor for the statistical gradient test. After, we get asymptotic skewness of the distribution of the maximum likelihood estimators of the model parameters. Finally, we show the asymptotic kurtosis coeficient of the distribution of the maximum likelihood estimators of the model parameters. Monte Carlo simulation studies are developed to evaluate the results obtained.

Nesta tese, desenvolvemos refinamentos assintóticos em modelos lineares generalizados heteroscedásticos (Smyth, 1989). Inicialmente, obtemos a matriz de covariâncias de segunda ordem dos estimadores de máxima verossimilhança corrigidos pelos viés de primeira ordem. Com base na matriz obtida, sugerimos modificações na estatística de Wald. Posteriormente, derivamos os coeficientes do fator de correção tipo-Bartlett para a estatística do teste gradiente. Em seguida, obtemos o coeficiente de assimetria assintótico da distribuição dos estimadores de máxima verossimilhança dos parâmetros do modelo. Finalmente, exibimos o coeficiente de curtose assintótico da distribuição dos estimadores de máxima verossimilhança dos parâmetros do modelo. Analisamos os resultados obtidos através de estudos de simulação de Monte Carlo. / In this thesis, we have developed asymptotic refinements in heteroskedastic generalized linear models (Smyth, 1989). Initially, we obtain the second-order covariance matrix for the maximum likelihood estimators corrected by the bias of first-order. Based on the obtained matrix, we suggest changes in Wald statistics. In addition, we derive the coeficients of the Bartlett-type correction factor for the statistical gradient test. After, we get asymptotic skewness of the distribution of the maximum likelihood estimators of the model parameters. Finally, we show the asymptotic kurtosis coeficient of the distribution of the maximum likelihood estimators of the model parameters. Monte Carlo simulation studies are developed to evaluate the results obtained.

<p>This doctoral thesis presents new ideas and research results on control of marine electric power system.</p><p>The main motivation for this work is the development of a control system, power management system (PMS) capable to improve the system robustness to blackout, handle major power system faults, minimize the operational cost and keep the power system machinery components under minimal stress in all operational conditions.</p><p>Today, the electric marine power system tends to have more system functionality implemented in integrated automation systems. The present state of the art type of tools and methods for analyzing marine power systems do only to a limited extent utilize the increased knowledge available within each of the mechanical and electrical engineering disciplines.</p><p>As the propulsion system is typically consisted of the largest consumers on the vessel, important interactions exists between the PMS and vessel propulsion system. These are interacted through the dynamic positioning (DP) controller, thrust allocation algorithm, local thruster controllers, generators' local frequency and voltage controllers. The PMS interacts with the propulsion system through the following main functions: available power static load control, load rate limiting control and blackout prevention control (i.e. fast load reduction). These functions serve to prevent the blackout and to ensure that the vessel will always have enough power.</p><p>The PMS interacts with other control systems in order to prevent a blackout and to minimize operational costs. The possibilities to maximize the performance of the vessel, increase the robustness to faults and decrease a component wear-out rate are mainly addressed locally for the individual control systems. The solutions are mainly implicative (for e.g. local thruster control, or DP thrust allocation), and attention has not been given on the interaction between these systems, the power system and PMS. Some of the questions that may arise regarding the system interactions, are as follows: how the PMS functionality may affect a local thruster control, how the local thruster control may affect the power system performance, how some consumers may affect the power system performance in normal operations and thus affect other consumers, how the power system operation may affect the susceptibility to faults and blackout, how various operating and weather conditions may affect the power system performance and thus propulsion performance though the PMS power limiting control, how propulsion performance may affect the overall vessel performance, which kind of faults can be avoided if the control system is re-structured, how to minimize the operational costs and to deal with the conflicting goals. This PhD thesis aims to provide answers to such questions.</p><p>The main contributions of this PhD thesis are:</p><p>− A new observer-based fast load reduction system for the blackout prevention control has been proposed. When compared to the existing fast load reduction systems, the proposed controller gives much faster blackout detection rate, high reliability in the detection and faster and more precise load reduction (within 150 miliseconds).</p><p>− New advanced energy management control strategies for reductions in the operational costs and improved fuel economy of the vessel.</p><p>− Load limiting controllers for the reduction of thruster wear-out rate. These controllers are based on the probability of torque loss, real-time torque loss and the thruster shaft</p><p>accelerations. The controllers provide means of redistributing thrust from load fluctuating thrusters to less load fluctuating ones, and may operate independently of the thrust allocation system. Another solution is also proposed where the load limiting controller based on thrust losses is an integrated part of DP thrust allocation algorithm.</p><p>− A new concept of totally integrated thrust allocation system, local thruster control and power system. These systems are integrated through PMS functionality which is contained within each thruster PLC, thereby distributed among individual controllers, and independent of the communications and dedicated controllers.</p><p>− Observer-based inertial controller and direct torque-loss controller (soft anti-spin controller) with particular attention to the control of machine wear-out rate. These controller contribute to general shaft speed control of electrical thrusters, generators and main propulsion prime movers.</p><p>The proposed controllers, estimators and concepts are demonstrated through time-domain simulations performed in MATLAB/SIMULINK. The selected data are typical for the required applications and may differ slightly for the presented cases.</p>

This doctoral thesis presents new ideas and research results on control of marine electric power system. The main motivation for this work is the development of a control system, power management system (PMS) capable to improve the system robustness to blackout, handle major power system faults, minimize the operational cost and keep the power system machinery components under minimal stress in all operational conditions. Today, the electric marine power system tends to have more system functionality implemented in integrated automation systems. The present state of the art type of tools and methods for analyzing marine power systems do only to a limited extent utilize the increased knowledge available within each of the mechanical and electrical engineering disciplines. As the propulsion system is typically consisted of the largest consumers on the vessel, important interactions exists between the PMS and vessel propulsion system. These are interacted through the dynamic positioning (DP) controller, thrust allocation algorithm, local thruster controllers, generators' local frequency and voltage controllers. The PMS interacts with the propulsion system through the following main functions: available power static load control, load rate limiting control and blackout prevention control (i.e. fast load reduction). These functions serve to prevent the blackout and to ensure that the vessel will always have enough power. The PMS interacts with other control systems in order to prevent a blackout and to minimize operational costs. The possibilities to maximize the performance of the vessel, increase the robustness to faults and decrease a component wear-out rate are mainly addressed locally for the individual control systems. The solutions are mainly implicative (for e.g. local thruster control, or DP thrust allocation), and attention has not been given on the interaction between these systems, the power system and PMS. Some of the questions that may arise regarding the system interactions, are as follows: how the PMS functionality may affect a local thruster control, how the local thruster control may affect the power system performance, how some consumers may affect the power system performance in normal operations and thus affect other consumers, how the power system operation may affect the susceptibility to faults and blackout, how various operating and weather conditions may affect the power system performance and thus propulsion performance though the PMS power limiting control, how propulsion performance may affect the overall vessel performance, which kind of faults can be avoided if the control system is re-structured, how to minimize the operational costs and to deal with the conflicting goals. This PhD thesis aims to provide answers to such questions. The main contributions of this PhD thesis are: − A new observer-based fast load reduction system for the blackout prevention control has been proposed. When compared to the existing fast load reduction systems, the proposed controller gives much faster blackout detection rate, high reliability in the detection and faster and more precise load reduction (within 150 miliseconds). − New advanced energy management control strategies for reductions in the operational costs and improved fuel economy of the vessel. − Load limiting controllers for the reduction of thruster wear-out rate. These controllers are based on the probability of torque loss, real-time torque loss and the thruster shaft accelerations. The controllers provide means of redistributing thrust from load fluctuating thrusters to less load fluctuating ones, and may operate independently of the thrust allocation system. Another solution is also proposed where the load limiting controller based on thrust losses is an integrated part of DP thrust allocation algorithm. − A new concept of totally integrated thrust allocation system, local thruster control and power system. These systems are integrated through PMS functionality which is contained within each thruster PLC, thereby distributed among individual controllers, and independent of the communications and dedicated controllers. − Observer-based inertial controller and direct torque-loss controller (soft anti-spin controller) with particular attention to the control of machine wear-out rate. These controller contribute to general shaft speed control of electrical thrusters, generators and main propulsion prime movers. The proposed controllers, estimators and concepts are demonstrated through time-domain simulations performed in MATLAB/SIMULINK. The selected data are typical for the required applications and may differ slightly for the presented cases.

Dans ce mémoire, nous étudions le problème de l'estimation de la variance pour les estimateurs par double dilatation et de calage pour l'échantillonnage à deux phases. Nous proposons d'utiliser une décomposition de la variance différente de celle habituellement utilisée dans l'échantillonnage à deux phases, ce qui mène à un estimateur de la variance simplifié. Nous étudions les conditions sous lesquelles les estimateurs simplifiés de la variance sont valides. Pour ce faire, nous considérons les cas particuliers suivants : (1) plan de Poisson à la deuxième phase, (2) plan à deux degrés, (3) plan aléatoire simple sans remise aux deux phases, (4) plan aléatoire simple sans remise à la deuxième phase. Nous montrons qu'une condition cruciale pour la validité des estimateurs simplifiés sous les plans (1) et (2) consiste à ce que la fraction de sondage utilisée pour la première phase soit négligeable (ou petite). Nous montrons sous les plans (3) et (4) que, pour certains estimateurs de calage, l'estimateur simplifié de la variance est valide lorsque la fraction de sondage à la première phase est petite en autant que la taille échantillonnale soit suffisamment grande. De plus, nous montrons que les estimateurs simplifiés de la variance peuvent être obtenus de manière alternative en utilisant l'approche renversée (Fay, 1991 et Shao et Steel, 1999). Finalement, nous effectuons des études par simulation dans le but d'appuyer les résultats théoriques. / In this thesis we study the problem of variance estimation for the double expansion estimator and the calibration estimators in the case of two-phase designs. We suggest to use a variance decomposition different from the one usually used in two-phase sampling, which leads to a simplified variance estimator. We look for the necessary conditions for the simplified variance estimators to be appropriate. In order to do so, we consider the following particular cases : (1) Poisson design at the second phase, (2) two-stage design, (3) simple random sampling at each phase, (4) simple random sampling at the second phase. We show that a crucial condition for the simplified variance estimator to be valid in cases (1) and (2) is that the first phase sampling fraction must be negligible (or small). We also show in cases (3) and (4) that the simplified variance estimator can be used with some calibration estimators when the first phase sampling fraction is negligible and the population size is large enough. Furthermore, we show that the simplified estimators can be obtained in an alternative way using the reversed approach (Fay, 1991 and Shao and Steel, 1999). Finally, we conduct some simulation studies in order to validate the theoretical results.

In this paper, we propose two types of sieve bootstrap, univariate and multivariate approach, for the generalized method of moments estimators of time series data. Compared with the nonparametric block bootstrap, the sieve bootstrap is in essence parametric, which helps fitting data better when researchers have prior information about the time series properties of the variables of interested. Our Monte Carlo experiments show that the performances of these two types of sieve bootstrap are comparable to the performance of the block bootstrap. Furthermore, unlike the block bootstrap, which is sensitive to the choice of block length, these two types of sieve bootstrap are less sensitive to the choice of lag length.

Made available in DSpace on 2016-06-02T20:04:52Z (GMT). No. of bitstreams: 1 6306.pdf: 1062380 bytes, checksum: de31a51e2d0a59e52556156a08c37b41 (MD5) Previous issue date: 2014-05-30 / Financiadora de Estudos e Projetos / In this work, we make a study of the Bayes sequential decision procedure applied to capture-recapture with fixed sample sizes, to estimate the size of a finite and closed population process. We present the statistical model, review the Bayesian decision theory, presenting the pure decision problem, the statistical decision problem and the sequential decision procedure. We illustrate the theoretical methods discussed using simulated data. / Neste trabalho, fazemos um estudo do procedimento de decisão sequencial de Bayes aplicado ao processo de captura-recaptura com tamanhos amostrais fixados, para estimação do tamanho de uma população finita e fechada. Apresentamos o modelo estatístico, revisamos a teoria de decisão bayesiana, apresentando o problema de decisão puro, o problema de decisão estatística e o procedimento de decisão sequencial. Ilustramos os métodos teóricos discutidos através de dados simulados.