The focus of this research is on hypotheses testing involving inequality constraints. In the first chapter of this dissertation, we propose Kolmogorov-Smirnov type tests for stochastic dominance relations between the potential outcomes of a binary treatment under the unconfoundedness assumption. Our stochastic dominance tests compare every point of the cumulative distribution functions (CDF), so they can fully utilize all information in the distributions. For first order stochastic dominance, the test statistic is defined as the supremum of the difference of two inverse-probability-weighting estimators for the CDFs of the potential outcomes. The critical values are approximated based on a simulation method. We show that our test has good size properties and is consistent in the sense that it can detect any violation of the null hypothesis asymptotically. First order stochastic dominance tests in the treated subpopulation, and higher order stochastic dominance tests in the whole population and among the treated are shown to share the same properties. The tests are applied to evaluate the effect of a job training program on incomes, and we find that job training has a positive effect on real earnings. Finally, we extend our tests to cases in which the unconfoundedness assumption does not hold. On the other hand, there has been a considerable amount of attention paid to testing inequality restrictions using Wald type tests. As noted by Wolak (1991), there are certain situations where it is difficult to obtain tests with correct size even asymptotically. These situations occur when the variance-covariance matrix of the functions in the constraints depends on the unknown parameters as would be the case in nonlinear models. This dependence on the unknown parameters makes it computationally difficult to find the least favorable configuration (LFC) which can be used to bound the size of the test. In the second chapter of this dissertation, we extend Hansen's (2005) superior predictive ability (SPA) test to testing hypotheses involving general inequality constraints in which the variance-covariance matrix can be dependent on the unknown parameters. For our test we are able to obtain correct size asymptotically plus test consistency without requiring knowledge of the LFC. Also the test can be applied to a wider class of problems than considered in Wolak (1991). In the last chapter, we construct new Kolmogorov-Smirnov tests for stochastic dominance of any pre-specified order without resorting to the LFC to improve the power of Barrett and Donald's (2003) tests. To do this, we first show that under the null hypothesis if the objects being compared at a given income level are not equal, then the objects at this given income level will have no effect on the null distribution. Second, we extend Hansen's (2005) recentering method to a continuum of inequality constraints and construct a recentering function that will converge to the underlying parameter function uniformly asymptotically under the null hypothesis. We treat the recentering function as a true underlying parameter function and add it to the simulated Brownian bridge processes to simulate the critical values. We show that our tests can control the size asymptotically and are consistent. We also show that by avoiding the LFC, our tests are less conservative and more powerful than Barrett and Donald's (2003). Monte Carlo simulations support our results. We also examine the performances of our tests in an empirical example. / text

No description available.

On s'intéresse au problème d'interpolation d'une fonction numérique d'une ou plusieurs variables réelles lorsque qu'elle est connue pour satisfaire certaines propriétés comme, par exemple, la positivité, monotonie ou convexité. Deux méthodes d'interpolation sont étudiées. D'une part, une approche déterministe conduit à un problème d'interpolation optimale sous contraintes linéaires inégalité dans un Espace de Hilbert à Noyau Reproduisant (RKHS). D'autre part, une approche probabiliste considère le même problème comme un problème d'estimation d'une fonction dans un cadre bayésien. Plus précisément, on considère la Régression par Processus Gaussien ou Krigeage pour estimer la fonction à interpoler sous les contraintes linéaires de type inégalité en question. Cette deuxième approche permet également de construire des intervalles de confiance autour de la fonction estimée. Pour cela, on propose une méthode d'approximation qui consiste à approcher un processus gaussien quelconque par un processus gaussien fini-dimensionnel. Le problème de krigeage se ramène ainsi à la simulation d'un vecteur gaussien tronqué à un espace convexe. L'analyse asymptotique permet d'établir la convergence de la méthode et la correspondance entre les deux approches déterministeet probabiliste, c'est le résultat théorique de la thèse. Ce dernier est vu comme unegénéralisation de la correspondance établie par [Kimeldorf and Wahba, 1971] entre estimateur bayésien et spline d'interpolation. Enfin, une application réelle dans le domainede l'assurance (actuariat) pour estimer une courbe d'actualisation et des probabilités dedéfaut a été développée. / This thesis is dedicated to interpolation problems when the numerical function is known to satisfy some properties such as positivity, monotonicity or convexity. Two methods of interpolation are studied. The first one is deterministic and is based on convex optimization in a Reproducing Kernel Hilbert Space (RKHS). The second one is a Bayesian approach based on Gaussian Process Regression (GPR) or Kriging. By using a finite linear functional decomposition, we propose to approximate the original Gaussian process by a finite-dimensional Gaussian process such that conditional simulations satisfy all the inequality constraints. As a consequence, GPR is equivalent to the simulation of a truncated Gaussian vector to a convex set. The mode or Maximum A Posteriori is defined as a Bayesian estimator and prediction intervals are quantified by simulation. Convergence of the method is proved and the correspondence between the two methods is done. This can be seen as an extension of the correspondence established by [Kimeldorf and Wahba, 1971] between Bayesian estimation on stochastic process and smoothing by splines. Finally, a real application in insurance and finance is given to estimate a term-structure curve and default probabilities.

This thesis presents three papers within the field of dynamic macroeconomics. The first paper, entitled “Medium-frequency cycles and the remarkable near trend-stationarity of output”, presents a dynamic stochastic general equilibrium model with endogenous growth, capable of reconciling the observed large medium-frequency fluctuations in output, with its long run (near) trend-stationarity. This requires a model in which standard business cycle shocks lead to highly persistent movements around trend, without significantly altering the trend itself. The robustness of the trend also requires that scale effects are eliminated both in the long and short runs. In an estimated version of the model, a financial-type shock to the stock of ideas emerges as the key driver of the medium frequency cycle. The second paper, entitled “Learning from learners”, is an intervention into two long running debates: the first, on whether learnability may be used to rule out explosive paths for inflation in New Keynesian models, and the second, into whether Taylor rule parameters may be identified from observing the data. We find that in an economy populated with traditional macroeconomic learners, Taylor rule parameters can always be identified by sophisticated econometric techniques. Furthermore, when all agents in the economy use such sophisticated techniques, stationary sunspot solutions are readily learnable, and there is no guarantee of convergence to a stationary solution even in the “determinate” case. This implies that learnability cannot be used for equilibrium selection. Finally, in the third paper, “Efficient simulation of DSGE models with inequality constraints” (joint with Michael Paetz), we present a new algorithm for the simulation of models subject to inequality constraints, such as the zero lower bound on nominal interest rates. Our algorithm is shown to deliver higher accuracy than all other non-global algorithms, and leading speed. We go on to provide a number of applications of our algorithm.

Made available in DSpace on 2015-03-04T18:50:51Z (GMT). No. of bitstreams: 1 Tese_Antonio_Boness.pdf: 1734195 bytes, checksum: 60769d0cc4e992347a83d1cf365a0030 (MD5) Previous issue date: 2007-08-02 / Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Apresentamos um modelo matemático geral, baseado na teoria de Cosserat para estruturas flexíveis unidimensionais, em regime de deslocamentos finitos e sujeitas a restrições unilaterais. Ao modelo geral agregamos a hipótese de inextensibilidade e, desprezando os efeitos do cisalhamento e das forças inerciais, formulamos o problema variacionalmente tanto na forma cinemática quanto em Lagrangiano Aumentado. Para esta última formulação, construímos aproximações por elementos finitos de Galerkin e utilizamos um algoritmo do tipo Uzawa para a solução do problema aproximado. Apresentamos estudos numéricos com o intuito de avaliar a formulação, validar o algoritmo de solução e exemplificar possíveis aplicações práticas do modelo. Buscando viabilizar uma análise numérica, realizamos uma linearização consistente do modelo geral apresentado anteriormente, produzindo um modelo em regime de pequenos deslocamentos e deformações, descrito no espaço tridimensional. Para este problema, introduzimos uma aproximação por elementos finitos mistos estabilizados, adicionando à formulação de Galerkin formas residuais de mínimos quadrados provenientes das equações de equilíbrio. Provamos que esta formulação atende às condições suficientes para existência e unicidade de solução, independente da esbeltez da estrutura. Apresentamos estimativas de erro indicando taxas de convergência e resultados numéricos comprovando tais taxas. Apresentamos algumas aplicações dos modelos ao estudo de estabilidade de dutos aquecidos e enterrados, na análise da estabilidade de armaduras de risers e umbilicais e, na área biológica, apontamos as possibilidades de suas utilizações na modelagem de moléculas de ADN.

Title: Optimization Problems under (max, min)-Linear Constraints and Some Related Topics. Author: Mahmoud Gad Department/Institue: Department of Probability and Mathematical Statis- tics Supervisor of the doctoral thesis: 1. Prof. RNDr. Karel Zimmermann,DrSc 2. Prof. Dr. Assem Tharwat, Cairo University, Egypt Abstract: Problems on algebraic structures, in which pairs of operations such as (max, +) or (max, min) replace addition and multiplication of the classical linear algebra have appeared in the literature approximately since the sixties of the last century. The first publications on these algebraic structures ap- peared by Shimbel [37] who applied these ideas to communication networks, Cunninghame-Green [12, 13], Vorobjov [40] and Gidffer [18] applied these alge- braic structures to problems of machine-time scheduling. A systematic theory of such algebraic structures was published probable for the first time in [14]. In recently appeared book [4] the readers can find latest results concerning theory and algorithms for (max, +)-linear systems of equations and inequalities. Since operation max replacing addition in no more a group, but a semigroup oppera- tion, it is a substantial difference between solving systems with variables on one side and systems with variables occuring on both sides of the equations....

Apresentamos um modelo matemático geral, baseado na teoria de Cosserat para estruturas flexíveis unidimensionais, em regime de deslocamentos finitos e sujeitas a restrições unilaterais. Ao modelo geral agregamos a hipótese de inextensibilidade e, desprezando os efeitos do cisalhamento e das forças inerciais, formulamos o problema variacionalmente tanto na forma cinemática quanto em Lagrangiano Aumentado. Para esta última formulação, construímos aproximações por elementos finitos de Galerkin e utilizamos um algoritmo do tipo Uzawa para a solução do problema aproximado. Apresentamos estudos numéricos com o intuito de avaliar a formulação, validar o algoritmo de solução e exemplificar possíveis aplicações práticas do modelo. Buscando viabilizar uma análise numérica, realizamos uma linearização consistente do modelo geral apresentado anteriormente, produzindo um modelo em regime de pequenos deslocamentos e deformações, descrito no espaço tridimensional. Para este problema, introduzimos uma aproximação por elementos finitos mistos estabilizados, adicionando à formulação de Galerkin formas residuais de mínimos quadrados provenientes das equações de equilíbrio. Provamos que esta formulação atende às condições suficientes para existência e unicidade de solução, independente da esbeltez da estrutura. Apresentamos estimativas de erro indicando taxas de convergência e resultados numéricos comprovando tais taxas. Apresentamos algumas aplicações dos modelos ao estudo de estabilidade de dutos aquecidos e enterrados, na análise da estabilidade de armaduras de risers e umbilicais e, na área biológica, apontamos as possibilidades de suas utilizações na modelagem de moléculas de ADN.

This research presents a Hybrid Particle Swarm Optimization with Bat Algorithm (HPSOBA) based approach to solve Optimal Reactive Power Dispatch (ORPD) problem. The primary objective of this project is minimization of the active power transmission losses by optimally setting the control variables within their limits and at the same time making sure that the equality and inequality constraints are not violated. Particle Swarm Optimization (PSO) and Bat Algorithm (BA) algorithms which are nature-inspired algorithms have become potential options to solving very difficult optimization problems like ORPD. Although PSO requires high computational time, it converges quickly; while BA requires less computational time and has the ability of switching automatically from exploration to exploitation when the optimality is imminent. This research integrated the respective advantages of PSO and BA algorithms to form a hybrid tool denoted as HPSOBA algorithm. HPSOBA combines the fast convergence ability of PSO with the less computation time ability of BA algorithm to get a better optimal solution by incorporating the BA’s frequency into the PSO velocity equation in order to control the pace. The HPSOBA, PSO and BA algorithms were implemented using MATLAB programming language and tested on three (3) benchmark test functions (Griewank, Rastrigin and Schwefel) and on IEEE 30- and 118-bus test systems to solve for ORPD without DG unit. A modified IEEE 30-bus test system was further used to validate the proposed hybrid algorithm to solve for optimal placement of DG unit for active power transmission line loss minimization. By comparison, HPSOBA algorithm results proved to be superior to those of the PSO and BA methods. In order to check if there will be a further improvement on the performance of the HPSOBA, the HPSOBA was further modified by embedding three new modifications to form a modified Hybrid approach denoted as MHPSOBA. This MHPSOBA was validated using IEEE 30-bus test system to solve ORPD problem and the results show that the HPSOBA algorithm outperforms the modified version (MHPSOBA). / Electrical and Mining Engineering / M. Tech. (Electrical Engineering)