Esta dissertação apresenta um estudo desenvolvido com o intuito de consolidar uma metodologia para a otimização de projeto de porta-sedes de uma válvula de esfera trunnion. Este trabalho está dividido em dois artigos. Primeiramente, é apresentado um estudo comparativo entre diferentes modelos de porta-sedes, realizado com o apoio do método dos elementos finitos (FEA). O porta-sede de melhor desempenho foi determinado utilizando a Função de Perda Quadrática Multivariada. O objetivo principal deste primeiro artigo é identificar os principais parâmetros da geometria de um porta-sede, que possam garantir o desempenho funcional da válvula e correspondente atendimento dos requisitos de qualidade. O segundo artigo descreve uma aplicação da metodologia de Projeto de Experimentos (DOE), conduzida com o intuito de identificar a configuração geométrica da válvula que conduza a condição ótima de funcionamento, fornecendo, desta forma, subsídio para a área de Desenvolvimento de Produtos na elaboração de válvulas mais robustas. Uma das principais contribuições deste trabalho é a constatação que os quatro fatores controláveis incluídos no estudo exercem efeito significativos sobre as variáveis de resposta utilizadas (pressão de contato e força de reação). Excetuando-se o fator “pressão de operação da válvula”, que caracteriza a condição operação, mas não é um parâmetro de projeto, o fator que revelou efeito mais pronunciado sobre as variáveis resposta foi a “área da pista de vedação”. / This thesis presents a study conducted in order to consolidate a methodology for seat-retainer design optimization of a trunnion ball valve. This work is divided in two papers. Initially a comparative study between different seat-retainer models, developed with the support of the finite element analysis (FEA), is presented. The best performance seat-retainer was determined using the Multivariate Quadratic Loss Function. The main purpose of this first article is to identify the main parameters of the seat-retainer geometry, which could ensure the functional performance of the valve and corresponding quality requirements. The second paper describes an application of Design of Experiments (DOE) methodology, conducted in order to identify the geometric configuration of the valve that leads to the optimal operating condition, providing thereby, contribution to the Product Development area in designing more robust valves. The main contribution of this work is the finding that the four control factors included in the study exert significant effect on the response variables used (contact pressure and reaction force). Except for the factor "valve operating pressure" that characterizes the operation condition, but is not a design parameter, the factor that showed more pronounced effect on the response variables was the “seat sealing area”.

This thesis consists of three papers that makes independent contributions to the fields of forecast evaluation and financial econometrics. As such, the papers, chapter 1-3, can be read independently of each other. In Chapter 1, “Inferring an agent’s loss function based on a term structure of forecasts”, we provide conditions for identification, estimation and inference of an agent’s loss function based on an observed term structure of point forecasts. The loss function specification is flexible as we allow the preferences to be both asymmetric and to vary non-linearly across the forecast horizon. In addition, we introduce a novel forecast rationality test based on the estimated loss function. We employ the approach to analyse the U.S. Government’s preferences over budget surplus forecast errors. Interestingly, we find that it is relatively more costly for the government to underestimate the budget surplus and that this asymmetry is stronger at long forecast horizons. In Chapter 2, “Monitoring Systemic Risk”, we define systemic risk as the conditional probability of a systemic banking crisis. This conditional probability is modelled in a fixed effect binary response panel-model framework that allows for cross-sectional dependence (e.g. due to contagion effects). In the empirical application we identify several risk factors and it is shown that the level of systemic risk contains a predictable component which varies through time. Furthermore, we illustrate how the forecasts of systemic risk map into dynamic policy thresholds in this framework. Finally, by conducting a pseudo out-of-sample exercise we find that the systemic risk estimates provided reliable early-warning signals ahead of the recent financial crisis for several economies. Finally, in Chapter 3, “Equity Premium Predictability”, we reassess the evidence of out-of- sample equity premium predictability. The empirical finance literature has identified several financial variables that appear to predict the equity premium in-sample. However, Welch & Goyal (2008) find that none of these variables have any predictive power out-of-sample. We show that the equity premium is predictable out-of-sample once you impose certain shrinkage restrictions on the model parameters. The approach is motivated by the observation that many of the proposed financial variables can be characterised as ’weak predictors’ and this suggest that a James-Stein type estimator will provide a substantial risk reduction. The out-of-sample explanatory power is small, but we show that it is, in fact, economically meaningful to an investor with time-invariant risk aversion. Using a shrinkage decomposition we also show that standard combination forecast techniques tends to ’overshrink’ the model parameters leading to suboptimal model forecasts.

Title: Modelling Bonus - Malus Systems Author: Marika Stroukalová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Lucie Mazurová, Ph.D., KPMS MFF UK Abstract: In this thesis we deal with bonus-malus tariff systems commonly used to adjust the a priori set premiums according to the individual claims during mo- tor third party liability insurance. The main aim of this thesis is to describe the standard model based on the Markov chain. For each bonus-malus class we also determine the relative premium ("relativity"). Another objective of this thesis is to find optimal values for the relativities taking into account the a priori set premiums. We apply the theoretical model based on the stationary distribu- tion of bonus-malus classes on real-world data and a particular real bonus-malus system used in the Czech Republic. The empirical part of this thesis compares the optimal and the real relativities and assesses the suitability of the chosen theoretical model for the particular bonus-malus system. Keywords: bonus-malus system, a priori segmentation, stationary distribution, relativity, quadratic loss function 1

Neste trabalho discutimos os principais argumentos da inferência bayesiana subjetivista. Posteriormente, a partir de uma revisão da literatura dos testes de hipóteses, os principais testes são analisados sob a ótica da teoria da decisão, particularmente no que tange às hipóteses precisas. Adicionalmente, funções de perda para testes de significância, seguindo a proposta de Fisher e do FBST, são analisadas e comparadas. / This work discusses the main points of the bayesian subjectivist inference. Posteriorly, from a literature review of hypothesis testing, the main approaches are interpreting from a decision-theoretic viewpoint, particularly regarding the precise hypotheses. Additionally, loss functions for tests of significance, following the proposal of Fisher and FBST, are analyzed and compared.

Neste trabalho discutimos os principais argumentos da inferência bayesiana subjetivista. Posteriormente, a partir de uma revisão da literatura dos testes de hipóteses, os principais testes são analisados sob a ótica da teoria da decisão, particularmente no que tange às hipóteses precisas. Adicionalmente, funções de perda para testes de significância, seguindo a proposta de Fisher e do FBST, são analisadas e comparadas. / This work discusses the main points of the bayesian subjectivist inference. Posteriorly, from a literature review of hypothesis testing, the main approaches are interpreting from a decision-theoretic viewpoint, particularly regarding the precise hypotheses. Additionally, loss functions for tests of significance, following the proposal of Fisher and FBST, are analyzed and compared.

近年來，田口方法的應用推廣與發展已經蔚為一股風潮，企業界許多設計工程師、生產現場的技術人員均普遍地使用田口方法，將品質設計於產品與生產製程之中，期能在商場上持續發展，並佔一席之地。然而，在以往田口方法的應用實例中，參數設計之因子水準的選取大都仰賴工程師憑著經驗來決定，但是經驗常會造成實驗的偏差，有鑒於此，本論文除了針對田口方法的使用做進一步的研究，並提出一套根據統計理論所推導出來的方法來協助工程師，使其在參數設計時對各因子水準的決定有一參考的依據，同時，為使其廣泛應用，本研究亦考慮到其它工業界常用的分配，而不再只侷限於常態分配。此外，本論文又針對SN比與損失函數之間的關係做進一步的討論，以使工業界能更深一層體會田口方法的優點及參數設計的目的。最後，本論文則研究非常態分配對損失函數及SN比估計值的影響情形，並表列各不同分配在α值給定之下，應如何決定樣本數(sample size)值，以使常態分配的假設更為合理。

We consider a principal components based decomposition of the expected value of the multivariate quadratic loss function, i.e., MQL. The principal components are formed by scaling the original data by the contents of the loss constant matrix, which defines the economic penalty associated with specific variables being off their desired target values. We demonstrate the extent to which a subset of these ``loss-scaled principal components", i.e., LSPC, accounts for the two components of expected MQL, namely the trace-covariance term and the off-target vector product. We employ the LSPC to solve a robust design problem of full and reduced dimensionality with deterministic models that approximate the true solution and demonstrate comparable results in less computational time. We also employ the LSPC to construct a test statistic called loss-scaled T^2 for multivariate statistical process control. We show for one case how the proposed test statistic has faster detection than Hotelling's T^2 of shifts in location for variables with high weighting in the MQL. In addition we introduce a principal component based decomposition of Hotelling's T^2 to diagnose the variables responsible for driving the location and/or dispersion of a subgroup of multivariate observations out of statistical control. We demonstrate the accuracy of this diagnostic technique on a data set from the literature and show its potential for diagnosing the loss-scaled T^2 statistic as well.

Model-based estimation techniques have been widely used in small area estimation. This thesis focuses on the Hierarchical Bayes (HB) estimation techniques in application to small area estimation for survey data. We will study the impact of applying spatial structure to area-specific effects and utilizing a specific generalized linear mixed model in comparison with a traditional Fay-Herriot estimation model. We will also analyze different loss functions with applications to a small area estimation problem and compare estimates obtained under these loss functions. Overall, for the case study under consideration, area-specific geographical effects will be shown to have a significant effect on estimates. As well, using a generalized linear mixed model will prove to be more advantageous than the usual Fay-Herriot model. We will also demonstrate the benefits of using a weighted balanced-type loss function for the purpose of balancing the precision of estimates with their closeness to the direct estimates.

Model-based estimation techniques have been widely used in small area estimation. This thesis focuses on the Hierarchical Bayes (HB) estimation techniques in application to small area estimation for survey data. We will study the impact of applying spatial structure to area-specific effects and utilizing a specific generalized linear mixed model in comparison with a traditional Fay-Herriot estimation model. We will also analyze different loss functions with applications to a small area estimation problem and compare estimates obtained under these loss functions. Overall, for the case study under consideration, area-specific geographical effects will be shown to have a significant effect on estimates. As well, using a generalized linear mixed model will prove to be more advantageous than the usual Fay-Herriot model. We will also demonstrate the benefits of using a weighted balanced-type loss function for the purpose of balancing the precision of estimates with their closeness to the direct estimates.

Uma questão interessante na política monetária é se os Bancos Centrais dão pesos iguais para desvios positivos e negativos da inflação e do hiato do produto das suas respectivas metas. Para responder à esta questão, estimou-se a função perda da autoridade monetária não parametricamente através do método de sieve estimator, expandindo-a através de uma base composta de polinômios ortogonais. A economia foi modelada com agentes foward-looking e com comprometimento por parte da autoridade monetária. O método foi aplicado para a os Estados Unidos desde 1960 e para o Brasil a partir de 1999. Para a economia norte-americana não foram encontradas evidências de assimetria nas preferências da autoridade monetária. Já no Brasil o Banco Central mostrou ter preferências assimétricas quanto à inflação, auferindo uma maior perda de desvios negativos do que positivos em relação à meta. / An interesting question in monetary policy is whether the Central Bank gives equal weights to positive and negative deviations of inflation and output gap from their targets. Trying answering this question, we estimated the monetary authority’s loss function nonparametrically, using the method of sieves, expanding it with orthogonal polynomials. The economy was model with forward-looking agents and with commitment of the monetary authority. We applied the method to U.S. monetary policy since 1960 and for Brazil since 1999. For the U.S. economy, it was not found evidence of asymmetry in the preferences of the monetary authority. In Brazil, the Central Bank proved to have asymmetric preferences about inflation, with a greater loss for negative deviations of inflation from the target rather for positive ones.