Em decorrência da inversão da pirâmide demográfica e a consequente queda das matrículas do ensino básico no Brasil, uma potencial medida de política pública é limitar o número de alunos por sala de aula. Nesse contexto, o objetivo principal deste estudo é avaliar o impacto de políticas que estipulem um número máximo de alunos por turma nas notas em Matemática e Português da Prova Brasil de alunos do 5º ano municipal da cidade de São Paulo e 9º estadual de todo o estado São Paulo. Para isso, empregou-se a metodologia de regressão descontínua fuzzy, utilizando o tamanho da sala predito pela função de Maimonides (Angrist e Lavy, 1999) como instrumento para o tamanho da sala observado. Os resultados mostram que não existam evidências estatisticamente significantes de que o tamanho da sala tenha impacto nas notas dos alunos. Visando trazer maior validade externa, o efeito de interesse foi estimado para o 5º e 9º ano estadual de Minas Gerais e Santa Catarina, e 5º ano estadual de São Paulo, obtendo-se a mesma conclusão. As análises de robustez performadas também concluem não haver efeito / As a result of the inversion of the demographic pyramid and the consequent drop in enrollments in basic education in Brazil, a possible public policy is to limit the number of students per classroom. In this context, the main objective of this study is to evaluate the impact of policies that stipulate a maximum number of students per class on students scores in Mathematics and Portuguese of Prova Brasil, using a sample of 5th and 9th grade students from the municipal and state school chains of São Paulo. Fuzzy regression discontinuity design was used to estimate these impacts, using predicted class size by the Maimonides rule (Angrist and Lavy, 1999) as an instrument for the actual class size. Results show that there is no statistically significant evidence that class size has an impact on student grades. Aiming to bring greater external validity, the effect of interest was estimated for the 5th and 9th grade of Minas Gerais and Santa Catarina, and 5th grade São Paulo, obtaining the same conclusion. The robustness analyzes performed also conclude that there is no effect.

Em decorrência da inversão da pirâmide demográfica e a consequente queda das matrículas do ensino básico no Brasil, uma potencial medida de política pública é limitar o número de alunos por sala de aula. Nesse contexto, o objetivo principal deste estudo é avaliar o impacto de políticas que estipulem um número máximo de alunos por turma nas notas em Matemática e Português da Prova Brasil de alunos do 5º ano municipal da cidade de São Paulo e 9º estadual de todo o estado São Paulo. Para isso, empregou-se a metodologia de regressão descontínua fuzzy, utilizando o tamanho da sala predito pela função de Maimonides (Angrist e Lavy, 1999) como instrumento para o tamanho da sala observado. Os resultados mostram que não existam evidências estatisticamente significantes de que o tamanho da sala tenha impacto nas notas dos alunos. Visando trazer maior validade externa, o efeito de interesse foi estimado para o 5º e 9º ano estadual de Minas Gerais e Santa Catarina, e 5º ano estadual de São Paulo, obtendo-se a mesma conclusão. As análises de robustez performadas também concluem não haver efeito / As a result of the inversion of the demographic pyramid and the consequent drop in enrollments in basic education in Brazil, a possible public policy is to limit the number of students per classroom. In this context, the main objective of this study is to evaluate the impact of policies that stipulate a maximum number of students per class on students scores in Mathematics and Portuguese of Prova Brasil, using a sample of 5th and 9th grade students from the municipal and state school chains of São Paulo. Fuzzy regression discontinuity design was used to estimate these impacts, using predicted class size by the Maimonides rule (Angrist and Lavy, 1999) as an instrument for the actual class size. Results show that there is no statistically significant evidence that class size has an impact on student grades. Aiming to bring greater external validity, the effect of interest was estimated for the 5th and 9th grade of Minas Gerais and Santa Catarina, and 5th grade São Paulo, obtaining the same conclusion. The robustness analyzes performed also conclude that there is no effect.

[pt] Este trabalho apresenta um modelo de Regressão Linear Nebulosa por Partes(RLNP). Trata-se de uma estrutura que envolve modelos de regressão linear por partes ponderadas por pertinências advindas da lógica nebulosa. Este modelo é comparado com o modelo de regressão linear. Os resultados mostram que o RLNP consegue identificar a estrutura não-linear dos dados simulados e que na maioria dos casos ele possui bom poder de ajuste. / [en] In this dissertation a Fuzzy Piece-Wise Linear Regressive model FPLieR is developed. The model´s structure combines linear regressive models with fuzzy logic´s grade of membership in a piece-wise fashion. A comparision is made between this model and the linear regression one. The results show that FPLieR is able to find the linear substructure of simulated data and that in most cases it presents a good fit.

目標：本文旨在建構一種新型的模糊回歸模式，解決一类較複雜的模糊回歸問題。 研究方法:推廣局部加權回歸的思想，先從理論上構建新模型；然後借由模拟數據，從多個方面考察新模型的性質，并和其他模型做比較。 發現：局部加權回歸方法結合模糊隸屬度概念，使模糊回歸理論有更多的應用場合。 原創性：目前在模糊回歸領域的主流思想是通過線性規劃等方法來構建模型，而本文另闢蹊徑，首次從局部加權的角度構建了模糊回歸的新模型。 關鍵字: 模糊理論 模糊回歸分析 局部加權 / Objective: This paper aims to construct a new fuzzy regression model to solve a more complex fuzzy regression problem. Method: Build a new model by promoting the idea of locally weighted regression; Using simulated data to compare the new model with other models. Conclusion: The fuzzy membership degree concept combined with the locally weighted regression method makes the fuzzy regression theory have more applications. Originality: At present, the main idea in the field of fuzzy regression is to construct models by means of linear programming. In this paper, a new model of fuzzy regression is constructed from the perspective of locally weighted method for the first time. Keyword: Fuzzy theory、 Fuzzy regression、Locally weighted method

動機與目的：傳統的統計迴歸模式假設觀測值的不確定性來自於隨機現象，而模糊迴歸則考慮不確定性來自於多重隸屬現象。不同的模型建構所得到的估計值也不一致。如何衡量模型的優劣程度，至今仍沒有一套嚴謹的標準。 研究方法：本研究以區間模糊數建構模糊迴歸模式，如此一來對樣本的解釋方式將更為貼近現實，並提出一套區間模糊數距離測度，以衡量估計值與實際值之間的差距。實證分析中（懸浮微粒PM_10濃度預測、台灣加權股價指數預測），我們藉由此距離測度衡量二維模糊迴歸與傳統二項最小平方法對於樣本的配適性。 創新與推廣：提出區間模糊數距離衡量估計值與原樣本之差異程度。在符合傳統統計迴歸精神之下，當距離最小就是差異最小的估計，最能符合所抽取的樣本，也是最佳估計。 重要發現：利用本區間模糊數距離測度，我們發現二維模糊迴歸方法比起傳統二項最小平方法更有效率且廣義殘差（generalized residual）將更小。 結論：過去以來，我們對於模糊迴歸架構一直都沒有完整的衡量標準。文中我們定義區間模糊數區間距離與平均距離，並推導賦距空間等性質。結合實例分析及應用，建構一合適模糊迴歸模式，以利統計決策分析參考。 / Objective: This study concerns how to develop effective fuzzy regression models. In the literature, little is addressed on how to evaluate the effectiveness of fuzzy regression models developed with different regression methods. We consider this issue in this work and present a framework for such evaluation. Method: We consider fuzzy regression models developed with different regression approaches. A method to evaluate the developed models is proposed. We then show that the proposed method possesses desirable mathematical properties and it is applied to compare the two-dimensional regression method and the traditional least square based regression method in our case studies: predicating the concentration of and the volatility of the weighted price index of the Taiwanese stock exchange. Innovation: We propose a new metric to define a distance between two fuzzy numbers. This metric can be used to evaluate the performance of different fuzzy regression models. When a prediction from one model is closest to the sample data measured in terms of the proposed metric, it can be recognized as the optimal predication. Results: Based on the proposed metric, it can be obtained that the two-dimensional fuzzy regression method is better than the traditional least square based regression method. Especially, its resulting generalized residual is smaller. Conclusion: In the literature, no unified framework has been previously proposed in evaluating the effectiveness of developed fuzzy regression models. In this work, we present a metric to achieve this goal. It facilitates the work to determine whether a fuzzy regression model suitably fits obtained samples and whether the model has potential to provide sufficient accuracy for follow-up analysis in a considered problem.

Submitted by Alessandro Ribeiro de Carvalho Casalecchi (alercc@gmail.com) on 2017-07-03T21:17:55Z No. of bitstreams: 1 Tese_Alessandro_Casalecchi.pdf: 2174297 bytes, checksum: 27298549cf220c58b7eb52f7323446d7 (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2017-07-04T11:10:20Z (GMT) No. of bitstreams: 1 Tese_Alessandro_Casalecchi.pdf: 2174297 bytes, checksum: 27298549cf220c58b7eb52f7323446d7 (MD5) / Made available in DSpace on 2017-07-05T13:46:08Z (GMT). No. of bitstreams: 1 Tese_Alessandro_Casalecchi.pdf: 2174297 bytes, checksum: 27298549cf220c58b7eb52f7323446d7 (MD5) Previous issue date: 2017-05-25 / Os dois artigos desta tese, os capítulos 2 e 3, referem-se a testes de hipótese mas têm focos diferentes. O capítulo 2, intitulado "Improvements for external validity tests in fuzzy regression discontinuity designs," apresenta condições --- hipóteses de continuidade, monotonicidade estrita e convergência pontual --- sob as quais testes de qualidade de ajuste para duas amostras podem ser usados para testes de validade externa em modelos de tratamento-controle que sofrem de "compliance" imperfeito. Modelos com "compliance" imperfeito permitem a estimação de efeitos de tratamento apenas para a subpopulação de "compliers", sendo que tais estimativas não são necessariamente válidas para outras subpopulações ("always-takers" e "never-takers"). Sob as condições do capítulo 2, o uso do teste de qualidade de ajuste no lugar do teste de diferença de médias representa um avanço para testes de validade externa, uma vez que mais hipóteses alternativas são detectáveis pelo primeiro teste. Sugerimos combinar duas estatísticas de teste de qualidade de ajuste (uma para tratados e outra para não tratados) na forma de um teste múltiplo ao invés de um teste conjunto. O capítulo 3, intitulado "Higher-order UMP tests", sugere uma estratégia para se escolher, dentro de um conjunto de estatísticas de teste disponíveis, aquela que fornece o teste mais poderoso quando as funções de poder dos testes em questão não podem ser diferenciadas através de métodos assintóticos usuais, como análise de poder local ("local power analysis"). Propomos o uso de aproximações assintóticas de ordem mais alta, como expansões de Edgeworth, para se aproximar as densidades amostrais das estatísticas disponíveis e, com isso, verificar-se quais delas possuem a propriedade da razão monotônica de verossimilhança. Tal propriedade implica, pelo Teorema de Karlin-Rubin, que o teste é uniformemente mais poderoso (UMP) --- ao menos até certa ordem de aproximação --- se a estatística for suficiente para o parâmetro relevante. Para o caso em que as estatísticas sendo comparadas não são suficientes, argumentamos que frequentemente elas podem se tornar suficientes para uma família paramétrica de interesse após reparametrizações apropriadas. Para fins de ilustração, nós aplicamos o método proposto para determinar o valor ótimo, em termos de poder, do parâmetro de suavização do estimador de densidade por kernel em bases de dados simuladas e concluímos que a ordem de aproximação usada nesta aplicação (segunda ordem) não é alta o suficiente para permitir a diferenciação das funções de poder associadas aos diferentes valores do parâmetro de suavização. / The two papers in this work, chapters 2 and 3, regard hypothesis testing but address different issues. Chapter 2, entitled "Improvements for external validity tests in fuzzy regression discontinuity designs", shows conditions --- assumptions of continuity, strict monotonicity and pointwise convergence --- under which two-sample goodness-of-fit (GOF) tests can be used to test for external validity in treatment-control models that suffer from imperfect compliance of units with respect to the assigned treatment. Imperfect compliance allows researchers to estimate only treatment effects for the subpopulation of compliers, and the validity of these estimates for other subpopulations (always-takers and never-takers) remains an open problem. Under the conditions in Chapter 2, the use of GOF tests in place of mean difference tests represents an improvement over other external validity tests in the literature, since more alternative hypotheses are detectable by the test statistic. We suggested to combine two GOF test statistics (one for the treated and one for the untreated) in a multiple test instead of a joint test. Chapter 3, entitled "Higher-order UMP tests", suggests a strategy to choose among candidate test statistics, according to a power criterion, when their power performances are not distinguishable by usual methods of asymptotic comparison like local power analysis. We propose the use of higher-order asymptotic expansions, like Edgeworth expansions, to approximate the sample densities of the candidate test statistics and verify which of them has the monotone likelihood ratio property. This property implies, by the Karlin-Rubin Theorem, that the test is uniformly most powerful (UMP) --- at least to an order of approximation --- if the statistic is sufficient for the relevant parameter. When the statistics under study are not sufficient, we argue that they can often be made sufficient for a desired parametric family after appropriate reparameterization. We applied the method to search for the power-optimal bandwidth for the kernel density estimator in simulated data sets, and concluded that the order of approximation that we used (second order) is still too low to allow us to distinguish among bandwidths.

傳統迴歸分析是假設觀測值的不確定性來自於隨機現象，本文則應用模糊隨機變數概念於迴歸模式的架構，考慮將隨機現象和模糊認知並列研究。針對樣本模糊數(x_i, Y_i)，我們進行模糊迴歸參數估計，並稱此為模糊迴歸模式分析。模糊迴歸參數估計大都採用線性規劃，求出適當區間，將觀測模糊數Y_i的分佈範圍全部覆蓋。但是此結果並不能充分反映觀測樣本Y_i的特性。本研究提出一套模糊迴歸參數的估計方法，其結果對觀測樣本的解釋將更為合理，且具有模糊不偏的特性。在分析過程中，我們亦提出一些模糊統計量如模糊期望值、模糊變異數、模糊中位數的定義，以增加對這些參數的模糊理解。最後在本文中也針對台灣景氣指標與經濟成長率作實務分析，說明模糊迴歸模式的適用性。 / Conventional study on the regression analysis is based on the conception that the uncertainty of observed data comes from the random property. However, in this paper we consider both of the random property and the fuzzy perception to construct the regression model by using of fuzzy random variables. For the fuzzy sample (x_i,Y_i), we will process the parameters estimation of the fuzzy regression, and we call this process as fuzzy regression analysis. The parameters estimation for a fuzzy regression model is generally derived by the linear programming scheme. But it's result usually doesn't sufficiently reflect the characteristics of the observed samples. Hence in this paper we propose an alternative technique for parameters estimation in constructing the fuzzy regression model. The result will describe the observed data better than the conventional method did, moreover it will have the fuzzy unbiased properties. For the purpose of fuzzy perception on the fuzzy random variables, we also give definitions for certain important fuzzy statistics such as fuzzy expected value, fuzzy variance and fuzzy median. Finally, we give an example about the Taiwan Business Cycle and the Taiwan Economic Growth Rate for illustration.

Knowledge about spatial and temporal variability of hydrological processes is central for sustainable water-resources management, and such knowledge is created from observational data. Hydrologic models are necessary for prediction for time periods and areas lacking data, but are affected by observational uncertainties. Methods for estimating and accounting for such uncertainties in water-resources modelling are of high importance, especially in regions such as Central America. Observational uncertainties were addressed in three ways in this thesis; quality control, quantitative estimation and development of model-evaluation techniques that addressed unquantifiable uncertainties. A first step in any modelling study should be the quality control and concurrent analysis of the representativeness of the observational data. In the characterisation of the precipitation regime in the Choluteca River basin in Honduras, four different quality problems were identified and 22% of the daily data had to be rejected. The monitoring network was found to be insufficient for a comprehensive characterisation of the high spatiotemporal variability of the precipitation regime. Quantitative estimations of data uncertainties can be made when sufficient information is available. Discharge-data uncertainties were estimated with a fuzzy regression for time-variable rating curves and from official rating curves for 35 stations in Honduras. The uncertainties were largest for low flows, as a result of measurement uncertainties and natural variability. A method for calibration with flow-duration curves was developed which enabled calibration to the whole flow range, accounting for discharge uncertainty and calibration with non-overlapping time periods for model input and evaluation data. The method compared favourably to traditional calibration in a test using two models applied in basins with different runoff-generation processes. A post-hoc analysis made it possible to identify potential model-structure errors and periods of disinformative data. Flow-duration curves were regionalised and used for calibration of a Central-American water-balance model. The initial model uncertainty for the ungauged basins was reduced by 70%. Non-representative precipitation data were found to be the main obstacle to comprehensive regional water-resources modelling in Central America. These methods bridged several problems related to observational uncertainties in water-balance modelling. Estimates of prediction uncertainty are an important basis for all types of decisions related to water-resources management. / Kännedom om hur hydrologiska processer varierar i tid och rum är grundläggande för hållbar vattenresursförvaltning och skapas utifrån observerade data. Hydrologiska modeller är nödvändiga för att förutsäga vattenbalansen för tidsperioder och områden utan data, men påverkas av observationsosäkerheter. Metoder för att hantera sådana osäkerheter i vattenresursmodellering är av stor betydelse i regioner såsom Centralamerika. Observationsosäkerheter hanterades på tre olika sätt i denna avhandling; kvalitetskontroll, kvantitativ uppskattning och utveckling av modellutvärderingsmetoder för beaktande av icke kvantifierbara osäkerheter. Ett viktigt första steg är kvalitetskontroll och samtidig analys av datas representativitet. Vid karaktäriseringen av nederbördsregimen i Cholutecaflodens avrinningsområde i Honduras identifierades fyra olika kvalitetsproblem och 22 % av data sorterades bort. Stationsnätet var otillräckligt för en fullödig karaktärisering av nederbördsregimens variationer i tid och rum. Dessa var mycket stora som ett resultat av komplexiteten hos de nederbördsgenererande mekanismerna. Kvantitativ uppskattning av observerade datas osäkerhet kan göras när tillräcklig information är tillgänglig. Osäkerheter i vattenföringsdata uppskattades dels vid beräkning av vattenföring med en oskarp regression för en tidsvariabel avbördningskurva, dels från en analys av officiella avbördningskurvor från 35 stationer i Honduras. Osäkerheten var i båda fallen högst vid låga flöden som ett resultat av högre mätosäkerheter samt större naturlig variabilitet än vid höga flöden. En metod för modellkalibrering med varaktighetskurvor utvecklades och gjorde det möjligt att kalibrera för hela flödesintervallet samtidigt, ta hänsyn till osäkerheter i vattenföringsdata samt kalibrera med icke överlappande driv- och utvärderingsdata. Metoden testades med två olika modeller i två avrinningsområden med olika avrinningsbildningsprocesser, och visade goda resultat jämfört med traditionell modellkalibrering. En post hoc-analys gjorde det möjligt att identifiera troliga modellstrukturfel och perioder med disinformativa data. Varaktighetskurvor regionaliserades och användes för kalibrering av en regional vattenbalansmodell för Centralamerika, varvid den initiala modellosäkerheten minskades med 70 %. Icke representativa nederbördsdata identifierades som det största hindret för regional vattenresursmodellering i Centralamerika. De metoder som utvecklades i detta arbete gör det möjligt att överbrygga ett flertal problem orsakade av bristfällig tillgänglighet och kvalitet av data och leder därmed till en förbättrad uppskattning av osäkerheten i vattenbalanssimuleringar. Sådana osäkerhetsskattningar är ett viktigt underlag vid alla typer av förvaltningsbeslut som rör vattenresurser.

Les politiques actives du marché du travail (PAMT) sont considérées de plus en plus comme nécessaires pour renforcer le lien entre protection sociale et création de sources de revenu plus durables dans l’objectif d’améliorer la qualité de l’emploi mais aussi, de façon plus générale, les conditions de vie. En conséquence, ces mesures jouent un rôle essentiel aujourd’hui dans les programmes de politique publique de la plupart des économies avancées et voient leur importance augmenter fortement dans les pays émergents et dans les pays en développement, où elles ne sont pas encore aussi bien établies. Il reste toutefois encore beaucoup à apprendre sur l’impact de ces mesures, en particulier sur le rôle des caractéristiques de leur mise en œuvre. Cette thèse entend contribuer à ce débat en étudiant l’efficacité des PAMT et le rôle des systèmes de mise en œuvre pour ce qui est de leur impact à la fois dans les pays développés et dans les pays émergents et en développement.Le premier chapitre examine sous un angle macroéconomique l’efficacité des PAMT à améliorer les résultats sur le marché du travail au sein des pays de l’OCDE, en particulier pour les travailleurs peu qualifiés. Il est capital de saisir de façon empirique l’effet net global des PAMT sur l’ensemble du marché du travail, car ces politiques entraînent souvent des phénomènes de substitution, de déplacement et d’autres conséquences indirectes. Les deux chapitres suivants cherchent à déterminer si les PAMT doivent être encore étendues dans les pays émergents et en développement. Pour ce faire, les effets au niveau individuel de deux types de PAMT en Amérique latine sont étudiés, en s’appuyant sur la présence de règles d’attribution intéressantes et de données de qualité au niveau individuel. Ainsi, le deuxième chapitre s’intéresse plus particulièrement aux conséquences à moyen et long terme d’un programme de workfare péruvien, l’une des mesures d’activation les moins étudiées, bien que fréquemment mise en œuvre dans la région, afin d’évaluer la durabilité de ses effets. Le troisième chapitre s’intéresse à l’introduction d’un ensemble complet de PAMT en Argentine, dans le but d’aider les bénéficiaires éligibles d’un programme de transfert de fonds sous conditions à trouver des sources de revenus plus stables. Dans les deux cas, l’accent est mis sur les effets sur la qualité de l’emploi et sur la manière dont la mise en œuvre des mesures conditionne leur impact.Ces travaux montrent que les PAMT sont utiles mais à condition qu’elles s’accompagnent d’une conception et d’une mise en œuvre appropriées. Les résultats confirment l’importance de ces facteurs pour ce qui est de l’efficacité des mesures tant dans les pays de l’OCDE que dans ceux d’Amérique latine étudiés. L’ampleur des effets dépend du type de mesure étudiée et de la catégorie de bénéficiaires visée. / Today, active labor market policies (ALMPs) are increasingly seen as a necessary tool to strengthen the link between social protection and the creation of more sustainable sources of income with a view to increasing work quality but also improving living conditions more broadly. As a result, the role of ALMPs in policy agendas remains high in most advanced economies and has increased dramatically in emerging and developing countries, where ALMPs are still less established. Despite this, there is still a lot to be learned regarding the impact of these policies, particularly with regards to the role of implementation characteristics. My dissertation aims to contribute to this debate by looking at the effectiveness of ALMPs and the role of delivery systems in shaping their impact in both, developed and emerging and developing countries.It starts by examining the effectiveness of ALMPs in OECD countries in improving labor market outcomes, especially for low-skilled individuals, from a macroeconomic perspective (Chapter 1). Capturing empirically the overall net effect of ALMPs on the wide labor market is of upmost importance, since the role of ALMPs frequently involves substitution, displacement and other indirect effects. Then, the following two chapters aim to assess whether ALMPs should be leveraged further in emerging and developing countries, by investigating the individual-level effects of two different types of ALMPs in Latin America, exploiting the availability of interesting assignment rules and good-quality individual-level data. Chapter 2 focuses on the medium- to long-term effects of a Peruvian workfare program, one of the least studied ALMPs in the region albeit commonly implemented, to assess the sustainability of these type of programs’ effects. Chapter 3 then looks at the provision of a comprehensive package of ALMPs in Argentina, implemented to support eligible beneficiaries of a conditional cash transfer program in finding more stable income opportunities. In both cases, the focus is placed on the effects on work quality and on the role of design and implementation in shaping the effects.My research suggests that ALMPs are relevant but mostly through appropriate design and implementation aspects. The results confirm the importance of these factors in ensuring effectiveness both in OECD and the Latin American countries assessed. The size of effects depends on the type of policy assessed and on the beneficiary group.