Este texto sugere sobre como calcular um tamanho de amostra com base no uso de um instrumento de coleta de dados formado por itens categóricos. Os argumentos para esta sugestão estão embasados nas teorias da Combinatória e da Paraconsistência. O propósito é sugerir um procedimento de cálculo simples e prático para obter um tamanho de amostra aceitável para coletar informações, organizá-las e analisar dados de uma aplicação de um instrumento de coleta de dados médicos baseado, exclusivamente, em itens discretos (itens categóricos), ou seja, cada item do instrumento é considerado como uma variável não-paramétrica com um número finito de categorias. Na Área de Saúde, é muito comum usar instrumentos para levantamento com base nesse tipo de itens: protocolos clínicos, registros hospitalares, questionários, escalas e outras ferramentas para inquirição consideram uma sequência organizada de itens categóricos. Uma fórmula para o cálculo do tamanho da amostra foi proposta para tamanhos de população desconhecidos e um ajuste dessa fórmula foi proposto para populações de tamanho conhecido. Pôde-se verificar, com exemplos práticos, a possibilidade de uso de ambas as fórmulas, o que permitiu considerar a praticidade de uso nos casos em que se tem disponível pouca ou nenhuma informação sobre a população de onde a amostra será coletada. / This text suggests how to calculate a sample size based on the use of a data collection instrument consisting of categorical items. The arguments for this suggestion are based on theories of Combinatorics and Paraconsistency. The purpose is to suggest a practical and simple calculation procedure to obtain an acceptable sample size to collect information, organize it and analyze data from an application of an instrument for collecting medical data, based exclusively on discrete items (categorical items), i.e., each item of the instrument is considered as a non-parametric variable with finite number of categories. In the health care it is very common to use survey instruments on the basis of such items: clinical protocols, hospital registers, questionnaires, scales and other tools for hearing consider a sequence of items organized categorically. A formula for calculating the sample size was proposed for a population of unknown size, and an adjusted formula has been proposed for population of known size. It was seen, with practical examples, the possibility of using both formulas, allowing to consider the practicality of the use in cases that have little or no information available about the population from which the sample is collected

Introdução: A poluição do ar pode levar a alterações no sistema respiratório, especialmente entre certos grupos, como as gestantes, que são mais vulneráveis aos efeitos de poluentes atmosféricos. A gravidez é um período que envolve alterações funcionais e anatômicas no corpo da mulher, incluindo alterações na função pulmonar, o que pode ser avaliado por espirometria, um método simples, barato e eficaz. Objetivos: Os objetivos deste estudo foram a usar a espirometria para avaliar a função pulmonar de mulheres no primeiro trimestre (T1) e no terceiro trimestre (T3) de gravidez e analisar a influência da exposição a poluição do ar sobre os parâmetros espirométricos. Metodologia: O estudo foi realizado no Ambulatório de Obstetrícia do Hospital das Clínicas da Faculdade de Medicina da Universidade de São Paulo (HCFMUSP) entre Maio de 2011 e Agosto de 2013. Foram aplicados os seguintes critérios de inclusão: gestação única, idade gestacional no dia da primeira espirometria inferior a 13,86 semanas, ausência de doenças maternas préexistentes, preparação adequada para o teste de espirometria e amostradores passivos individuais (APIs) adequados para análise. Os critérios de exclusão foram a mudança de endereço, o aborto, o teste de espirometria inadequado e desistência de participar do projeto. Os APIs contendo dois filtros de celulose embebidos com solução absorvente para capturar os níveis de NO2 e outros dois filtros embebidos com solução de índigo blue para medir os níveis de O3 foram entregues às gestantes cerca de 12 dias antes da realização do teste de espirometria. Dados do relatório anual da Companhia Ambiental do Estado de São Paulo (CETESB) para o mesmo período dos amostradores passivos, foram utilizados. Para a espirometria, um espirômetro Koko foi utilizado, sendo considerada as duas melhores curvas para avaliar os resultados da função pulmonar. Análise estatística: Foi utilizado o teste Mann-Whitney para grupos independentes e Wilcoxon para os dependentes. Devido à pequena variação na exposição à poluição, a exposição no primeiro trimestre (Q1) e quarto trimestre (Q4) foram comparados para cada poluente em T1 e T3 através da análise nãoparamétrica para medidas repetidas. Resultados: Houve uma redução estatisticamente significativa dos valores absolutos (T1: 3,690 L; T3: 3,475 L) e preditos (T1: 101%, T3: 97,5%) da capacidade vital forçada (CVF), p < 0,0001. E uma redução estatisticamente significativa dos valores absolutos (T1: 3.080 L; T3: 2.950 L) e preditos (T1: 99%, T3: 96%) do volume expiratório forçado no primeiro segundo do procedimento (FEV1), p < 0,0001. A exposição à poluição foi semelhante em ambos os trimestres, exceto para a exposição de NO2 no API, o que foi inferior em T3 (p = 0,001). Independentemente do trimestre (T1 ou T3), o grupo de mulheres do Q4 (T1: 97,5%; T3: 98,5%) teve NO2 estatisticamente maior dos valores do fluxo expiratório forçado de 25 a 75% do procedimento (FEF25-75%) do que o grupo em Q1 (T1: 80%; T3: 92%). O grupo de mulheres do Q1 do NO2 teve um aumento significativo neste parâmetro de T1 a T3 (p = 0,042). Em termos de valores absolutos da relação FEV1/FVC, o grupo de mulheres no Q1 mostrou um aumento estatisticamente significativo neste parâmetro de T1 (0,810 L) para T3 (0,840 L) (p = 0,026). Em T3, os valores absolutos e relativos da CVF foram estatisticamente maiores para o grupo de gestantes do Q4 (3,535 L; 100,5%) de NO2 do que para o grupo de gestantes do Q1 (3,345 L; 92%). O grupo de gestantes do Q4 de O3 mostrou o VEF1 estatisticamente maior eno T1 (102,5%) do que no T3 (95,5%) (p < 0,001). Independentemente do trimestre, o grupo de gestantes do Q4 do MP10, teve valores absolutos da CVF (T1: 3.520 L; T3: 3,265 L) e os valores de VEF1 (T1: 2,915 L; T32.840 L) foram estatisticamente menor do que para o grupo em Q1 (FVC - T1: 3.780 L; T3: 3.580 L) (FEV1 - T1: 3.180 L; T3: 3.065 L) p = 0,040; p = 0,035, respectivamente. Valores absolutos e preditos do pico de fluxo expiratório (PEF) em T1 das mulheres do Q4 (5,995 L; 80%) do MP10 foram estatisticamente menores do que para as mulheres no Q1 (6,675 L; 85%) (p = 0,006; p = 0,041 , respectivamente). Mulheres grávidas em Q4 (0,835 L) do MP10 tiveram os valores da relação VEF1/CVF estatisticamente menores valores do que as mulheres do Q1 (0,850 L) (p = 0,029). Conclusão: Exposição a NO2 e O3 foi associada com o aumento de alguns dos parâmetros de espirometria, indicando a presença de uma possível função de defesa pulmonar ou mecanismo compensatório em mulheres grávidas, quando expostos a esses poluentes. O MP10 foi associado com a redução de alguns parâmetros de espirometria durante a gravidez, indicando os efeitos danosos do poluente para a função do pulmão de mulheres grávidas / Introduction - Air pollution can lead to alterations to the respiratory system, particularly among certain groups, such as pregnant women, which are more vulnerable to the effects of air pollutants. Pregnancy is a period involving functional and anatomical changes in a woman\'s body. These changes include pulmonary function, which can be assessed by spirometry, a simple, inexpensive and effective method. Objectives - The aims of this study were to use spirometry to evaluate pulmonary function in pregnant women in the first trimester (T1) and the third trimester (T3) of pregnancy and to analyze the influence of air pollution exposure on the spirometry parameters. Methodology - This study was carried out at the Obstetrics Clinic of Hospital das Clínicas da Faculdade de Medicina da Universidade de São Paulo (HCFMUSP) between May 2011 and August 2013. The following inclusion criteria were applied: singleton pregnancy, 13.86 weeks gestational age at the first spirometry, no preexisting maternal diseases, adequate preparation for the spirometry test and individual passive samplers (IPAs) suitable for analysis. The exclusion criteria were change of address, abortion, inadequate spirometry testing and withdrawal from the project. The exposure to pollutants prior to the spirometry tests was assessed in T1 and T3. The passive samplers containing two cellulose filters soaked with absorbent solution to capture NO2 levels and two other filters soaked with indigo solution to measure O3 levels were provided to the pregnant women roughly 12 days prior to the spirometry test. Data from the environmental Company of São Paulo State (CETESB) annual report for the same period the passive samplers were used. For the spirometry, a Koko spirometer was used, taking the two best curves to assess lung function results. Statistical Analysis - We used Mann- Whitney tests for independent groups and Wilcoxon for the dependent ones. Due to the small variation in the exposure to pollution, exposure in the first quarter (Q1) and fourth quarter (Q4) were compared for each pollutant in T1 and T3 through non-parametrical analysis for repeated measurements. Results - It has been noted a significant statistical reduction of absolute and predicted forced vital capacity (FVC) values (3.690 L; 3.475 L) and forced expiratory volume during the first second of the procedure (FEV1) (3.080 L; 2.950 L) from T1 to T3. Exposure to pollution was similar in both trimesters, except for exposure to NO2 in the passive sampler, which was lower in T3 (p = 0.001). Regardless of the trimester (T1 or T3), the group of pregnant women in Q4 (97.5%; 98.5%) of NO2 had statistically higher predicted forced expiratory values of 25 to 75% of the procedure (FEF25-75%) than the group in Q1 (80%; 92%). Pregnant women in Q1 of NO2 had a significant increase in this parameter from T1 to T3 (p = 0.042). In terms of absolute FEV1/FVC values, pregnant women in Q1 showed a statistically significant rise in this parameter from T1 (0.810 L) to T3 (0,840 L) (p = 0,026). In T3, absolute and predicted FVC values were statistically higher for the group of pregnant women in Q4 (3.535 L; 100.5%) of NO2 than for the group of pregnant women in Q1 (3.345 L; 92%). Pregnant women in Q4 of O3 displayed statistically higher FEV1 values in T1 (102.5%) than in T3 (95.5%) (p < 0.001). Regardless of trimester, for the group of pregnant women in Q4 of MP10, absolute FVC (T1:3 .520 L; T3: 3.265 L) and FEV1 values (T1: 2.915 L; T3: 2.840 L) were statistically lower than for the group in Q1 (FVC - T1: 3.780 L; T3: 3.580 L) (FEV1 - T1: 3.180 L; T3: 3.065 L) p = 0.040; p = 0.035 respectively. Absolute and predicted peak expiratory flow (PEF) in T1 of pregnant women in Q4 (5.995 L; 80%) of MP10 were statistically lower than for the pregnant women in Q1 (6.675 L; 85%) (p = 0.006; p = 0.041, respectively). Pregnant women in Q4 (0.835 L) of MP10 displayed statistically lower absolute FEV1/FVC values than the pregnant women in Q1 (0.850 L) (p = 0.029). Conclusion - Exposure to NO2 and O3 was associated with the increase in some of the spirometry parameters, indicating the presence of a possible lung function defense or compensatory mechanism in pregnant women when exposed to those pollutants. The MP10 was associated with the reduction of some spirometry parameters during pregnancy, indicating the harmful effects of that pollutant to the lung function of pregnant women

OBJETIVO: Investigar a relação entre força muscular e função motora, em pacientes com DMD, em um período de 4 anos consecutivos, a partir de avaliações semestrais. MÉTODO: A força muscular foi medida por meio de testes manuais e o cálculo por grupo muscular seguiu o proposto pelo Medical Research Council (MRC) e a função motora pelo método de Medida da Função Motora (MFM), em 43 pacientes (8-30 anos). Foi realizada uma análise descritiva e o teste de correlação de Spearman. Foram investigadas as relações entre pontuações totais e parciais da MRC e da MFM. RESULTADOS: O estudo evidenciou correlações classificadas de moderada a forte relação entre a força muscular e função motora, principalmente com o escore total da MFM e a dimensão D2 (musculatura axial e função motora proximal). Foi encontrada relação negativa moderada entre idade e essas variáveis. CONCLUSÃO: A perda progressiva da função motora tem relação direta e proporcional com a diminuição da força muscular. Quanto maior a idade do paciente, pior sua função motora e força muscular, fornecendo com essa informação, indicadores adicionais da progressão da doença / OBJECTIVE: This study investigated this relationship and examined whether muscle strength and/or motor function would be related to age in DMD. METHODS: Muscle strength was measured by the Medical Research Council scale (MRC) and motor function by the Motor Function Measure (MFM) in 43 patients (8-30 yrs). Spearman tests, descriptive analysis, investigated the relationships between total/ partial scores of MRC and MFM. RESULTS: Total MRC and MFM scores were strongly related to each other and moderately related to age. Many strong relationships between partial MRC and MFM scores were found, mostly between partial MRC scores and MFM dimension 2 (axial and proximal motor function). CONCLUSION: It is possible to predict that the progressive loss of motor function has direct relationship to decreased muscle strength. That the older the patient, the worse their motor function and muscle strength, providing with this information, additional indicators of disease progression

Este trabalho se propõe analisar a relação entre o investimento em saúde e desenvolvimento dos estados brasileiros - medido pelo Índice de Desenvolvimento Humano- (IDH) mediante a utilização da tecnologia de produção denominada FDH (Free Disposal Hull - Fronteira com livre descarte de recursos). Para os estados não eficientes, serão identificados os percentuais de alteração dos insumos necessários para que estados sejam eficientes. Na seqüência, são selecionados os estados eficientes e com baixo índice de desenvolvimento, para serem utilizados pelos governos estadual e federal como prioridade em uma política de desenvolvimento para o Estado brasileiro, uma vez que, esses estados, por serem eficientes, com o aumento de investimento em ativos de saúde, aumentarão seu índice de desenvolvimento. Em suma, tem-se que os resultados permitirão algumas considerações sobre a eficiência em alocação de recursos nos diferentes ativos de saúde, possibilitando auxiliar a tomada de decisão do gestor público, no que diz respeito à alocação dos recursos disponíveis para área da saúde. / In this work it has attempted to appraise, quantitatively, the efficiency levels of the brazilians states. It is analyzed the relationship between output (development) and inputs (Health Assets) by constructing nonparametric efficiency frontiers. The technique of efficiency analysis were used to determine this frontier is the FDH approach. For the not efficient states, the percentages of alteration of inputs will be identified (Health Assets) necessary so that states are efficient. In the sequence, the efficient states and with low index of development will be selected, to be used for the state and federal governments as priority in one politics of Brazil development, a time that, these states, for being efficient, with the increase of investment in health asset, will increase its index of development. The results will be provided useful insights into the assessment of the administrative efficiency Health Assets.

Nesta tese consideramos um modelo de regressão não paramétrica, quando a variável explicativa e um processo estritamente estacionário e alpha-mixing. São estudadas as condições sobre o processo Xt e sua estrutura de dependência, assim como do domínio da função f a ser estimada. Também são feitas as adaptações necessárias aos procedimentos para obter as taxas de convergência do risco para a norma Lp, no caso de ondaletas deformadas. Em relação às ondaletas adaptativas de Haar, obtêm-se as taxas de convergência do risco do estimador proposto. Mediante estudos de simulação, e avaliado o desempenho dos procedimentos propostos quando aplicados a amostras finitas sob diferentes níveis de perturbação do sinal e diferentes tamanhos da amostra. Também são feitas aplicações a dados reais. / In this thesis we consider a nonparametric regression model, when the exploratory variables are alpha-mixing stationary processes. We obtain convergence rates for risk for Lp norm, via warped wavelets, under suitable regularity conditions. For estimation using design adapted Haar wavelets we obtain convergence rates for the risk of the proposed estimator. The performance of the estimators are assessed via simulation studies with dierent sample sizes and dierent signal-to-noise ratios. Applications to real data are also given.

Die Dissertation ``Asymptotische \Äquivalenz f\ür ein Modell unabh\ängiger nicht identisch verteilter Daten'' besch\äftigt sich mit der Le Camschen Theorie der Experimente. Le Cam hat den sogenannten $\Delta$-Abstand zwischen statistischen Experimenten definiert; ist dieser Abstand f\ür zwei Modelle klein, so sind ihre statistischen Eigenschaften \ähnlich. Zwei Folgen von Experimenten nennt man asymptotisch \äquivalent, falls ihr $\Delta$-Abstand gegen Null konvergiert.\\ In dieser Arbeit beweisen wir asymptotische \Äquivalenz zwischen einem Modell mit unabh\ängigen, nicht identisch verteilten Beobachtungen und einem Gaußschen Shift-Modell. Die i-te Beobachtung des ersten Experimentes ist dabei gem\äß einer Dichte $h(i/n,.)$ verteilt, wobei die Funktion h eine Schar von Dichten bildet. Wir approximieren also ein kompliziertes statistisches Experiment durch ein einfacheres, n\äymlich ein Gaußsches Shift-Modell. Die Dichten h geh\ören einer Menge h\ölderstetiger Funktionen an, so daß wir es mit einem nichtparametrischen Problem zu tun haben. Das von uns bewiesene \Äquivalenzresultat kann auch als eine nichtparametrische Version der ebenfalls von Le Cam eingef\ührten LAN Bedingung aufgefaßt werden. Ein wichtiges Hilfsmittel zum Beweis des oben beschriebenen Resultats ist das sogenannte Coupling von stochastischen Prozessen, d.h. die Konstruktion solcher Prozesse auf einem gemeinsamen Wahrscheinlichkeitsraum, so daß die Prozesse nahe beieinander liegen. Im zweiten Teil der Arbeit beweisen wir eine funktionale Version eines solchen Coupling Resultats f\ür den sequentiellen empirischen Prozeß und den Kiefer-M\üller Prozeß unter Verwendung der sogenannten Ungarischen Konstruktion. / The thesis "Asymptotic Equivalence of Experiments for a Model with Independent and Nonidentically distributed Observations" deals with the theory of experiments that was developped by Le Cam. \\ Le Cam defined the so called $\Delta$-distance between experiments. If this distance is small for two given models it means that their statistical properties are similar. We call two sequences of experiments asymptotic equivalent if their $\Delta$-distance converges to zero.\\ In this thesis we prove asymptotic equivalence between a model with independent and nonidentically distributed observations and a Gaussian shift model. The i-th observation in the first model is distributed according to a density $h(i/n,.)$ where $h$ is a bunch of densities on the unit interval. This means that we approximate a complicated statistical experiment by a simpler one, namely a Gaussian shift model. The densites h belong to a H\"older ball such that we have a nonparametric problem. Our result can also be viewed as a nonparametric version of the LAN property which was also defined by Le Cam. An important tool for proving our result is the coupling of stochastic processes, i.e. the construction of processes on a common probability space such that they are close in a strong sense. In the second part of the thesis we prove a functional version of such a coupling result for the sequential empirical process and the Kiefer-M\"uller process by using the Hungarian construction.

Diese Dissertation betrachtet das Problem der nichtparametrischen Schätzung der Diffusionskoeffizienten eines ein-dimensionalen und zeitlich homogenen Itô-Diffusionsprozesses. Dabei werden verschiedene diskrete Sampling Regimes untersucht. Im ersten Teil zeigen wir, dass eine Variante des von Gobet, Hoffmann und Reiß konstruierten Niedrigfrequenz-Schätzers auch im Fall von zufälligen Beobachtungszeiten verwendet werden kann. Wir beweisen, dass der Schätzer optimal im Minimaxsinn und adaptiv bezüglich der Verteilung der Beobachtungszeiten ist. Außerdam wenden wir die Lepski Methode an um einen Schätzer zu erhalten, der zusätzlich adaptiv bezüglich der Sobolev-Glattheit des Drift- und Volatilitätskoeffizienten ist. Im zweiten Teil betrachten wir das Problem der Volatilitätsschätzung für äquidistante Beobachtungen. Im Fall eines stationären Prozesses, mit kompaktem Zustandsraum, erhalten wir einen Schätzer, der sowohl bei hochfrequenten als auch bei niedrigfrequenten Beobachtungen die optimale Minimaxrate erreicht. Die Konstruktion des Schätzers beruht auf spektralen Methoden. Im Fall von niedrigfrequenten Beobachtungen ist die Analyse des Schätzers ähnlich wie diejenige in der Arbeit von Gobet, Hoffmann und Reiß. Im hochfrequenten Fall hingegen finden wir die Konvergenzraten durch lokale Mittelwertbildung und stellen daubt eine Verbindung zum Hochfrequenzschätzer von Florens-Zmirou her. In der Analyse unseres universalen Schätzers benötigen wir scharfe obere Schranken für den Schätzfehler von Funktionalen der Occupation time für unstetige Funktionen. Wir untersuchen eine auf Riemannsummen basierende Approximation der Occupation time eines stationären, reversiblen Markov-Prozesses und leiten obere Schranken für den quadratischen Fehler her. Im Fall von Diffusionsprozessen erhalten wir Konvergenzraten für Sobolev Funktionen. / In this thesis, we consider the problem of nonparametric estimation of the diffusion coefficients of a scalar time-homogeneous Itô diffusion process from discrete observations under various sampling assumptions. In the first part, the low-frequency estimation method proposed by Gobet, Hoffmann and Reiß is modified to cover the case of random sampling times. The estimator is shown to be optimal in the minimax sense and adaptive to the sampling distribution. Moreover, Lepski''s method is applied to adapt to the unknown Sobolev smoothness of the drift and volatility coefficients. In the second part, we address the problem of volatility estimation from equidistant observations without a predefined frequency regime. In the case of a stationary diffusion with compact state space and boundary reflection, we introduce a universal estimator that attains the minimax optimal convergence rates for both low and high-frequency observations. Being based on the spectral method, the low-frequency analysis is similar to the study conducted by Gobet, Hoffmann and Reiß. On the other hand, the derivation of the convergence rates in the high-frequency regime requires local averaging of the low-frequency estimator, which makes it mimic the behaviour of the classical high-frequency estimator introduced by Florens-Zmirou. The analysis of the universal estimator requires tight upper bounds on the estimation error of the occupation time functional for non-continuous functions. In the third part of the thesis, we thus consider the Riemann sum approximation of the occupation time functional of a stationary, time-reversible Markov process. Upper bounds on the squared mean estimation error are provided. In the case of diffusion processes, convergence rates for Sobolev regular functions are obtained.

L’objectif de cette thèse est de construire des estimateurs non-paramétriques d’une fonction de distribution, d’une densité de probabilité et d’une fonction de régression en utilisant les méthodes d’approximation stochastiques afin de corriger l’effet du bord créé par les estimateurs à noyaux continus classiques. Dans le premier chapitre, on donne quelques propriétés asymptotiques des estimateurs continus à noyaux. Puis, on présente l’algorithme stochastique de Robbins-Monro qui permet d’introduire les estimateurs récursifs. Enfin, on rappelle les méthodes utilisées par Vitale, Leblanc et Kakizawa pour définir des estimateurs d’une fonction de distribution et d’une densité de probabilité en se basant sur les polynômes de Bernstein.Dans le deuxième chapitre, on a introduit un estimateur récursif d’une fonction de distribution en se basant sur l’approche de Vitale. On a étudié les propriétés de cet estimateur : biais, variance, erreur quadratique intégré (MISE) et on a établi sa convergence ponctuelle faible. On a comparé la performance de notre estimateur avec celle de Vitale et on a montré qu’avec le bon choix du pas et de l’ordre qui lui correspond notre estimateur domine en terme de MISE. On a confirmé ces résultatsthéoriques à l’aide des simulations. Pour la recherche pratique de l’ordre optimal, on a utilisé la méthode de validation croisée. Enfin, on a confirmé les meilleures qualités de notre estimateur à l’aide des données réelles. Dans le troisième chapitre, on a estimé une densité de probabilité d’une manière récursive en utilisant toujours les polynômes de Bernstein. On a donné les caractéristiques de cet estimateur et on les a comparées avec celles de l’estimateur de Vitale, de Leblanc et l’estimateur donné par Kakizawa en utilisant la méthode multiplicative de correction du biais. On a appliqué notre estimateur sur des données réelles. Dans le quatrième chapitre, on a introduit un estimateur récursif et non récursif d’une fonction de régression en utilisant les polynômes de Bernstein. On a donné les caractéristiques de cet estimateur et on les a comparées avec celles de l’estimateur à noyau classique. Ensuite, on a utilisé notre estimateur pour interpréter des données réelles. / The aim of this thesis is to construct nonparametric estimators of distribution, density and regression functions using stochastic approximation methods in order to correct the edge effect created by kernels estimators. In the first chapter, we givesome asymptotic properties of kernel estimators. Then, we introduce the Robbins-Monro stochastic algorithm which creates the recursive estimators. Finally, we recall the methods used by Vitale, Leblanc and Kakizawa to define estimators of distribution and density functions based on Bernstein polynomials. In the second chapter, we introduced a recursive estimator of a distribution function based on Vitale’s approach. We studied the properties of this estimator : bias, variance, mean integratedsquared error (MISE) and we established a weak pointwise convergence. We compared the performance of our estimator with that of Vitale and we showed that, with the right choice of the stepsize and its corresponding order, our estimator dominatesin terms of MISE. These theoretical results were confirmed using simulations. We used the cross-validation method to search the optimal order. Finally, we applied our estimator to interpret real dataset. In the third chapter, we introduced a recursive estimator of a density function using Bernstein polynomials. We established the characteristics of this estimator and we compared them with those of the estimators of Vitale, Leblanc and Kakizawa. To highlight our proposed estimator, we used real dataset. In the fourth chapter, we introduced a recursive and non-recursive estimator of a regression function using Bernstein polynomials. We studied the characteristics of this estimator. Then, we compared our proposed estimator with the classical kernel estimator using real dataset.

Lokal parametrische Modelle werden häufig im Kontext der nichtparametrischen Schätzung verwendet. Bei einer punktweisen Schätzung der Zielfunktion können die parametrischen Umgebungen mithilfe von Gewichten beschrieben werden, die entweder von den Designpunkten oder (zusätzlich) von den Beobachtungen abhängen. Der Vergleich von verrauschten Beobachtungen in einzelnen Punkten leidet allerdings unter einem Mangel an Robustheit. Der Propagations-Separations-Ansatz von Polzehl und Spokoiny [2006] verwendet daher einen Multiskalen-Ansatz mit iterativ aktualisierten Gewichten. Wir präsentieren hier eine theoretische Studie und numerische Resultate, die ein besseres Verständnis des Verfahrens ermöglichen. Zu diesem Zweck definieren und untersuchen wir eine neue Strategie für die Wahl des entscheidenden Parameters des Verfahrens, der Adaptationsbandweite. Insbesondere untersuchen wir ihre Variabilität in Abhängigkeit von der unbekannten Zielfunktion. Unsere Resultate rechtfertigen eine Wahl, die unabhängig von den jeweils vorliegenden Beobachtungen ist. Die neue Parameterwahl liefert für stückweise konstante und stückweise beschränkte Funktionen theoretische Beweise der Haupteigenschaften des Algorithmus. Für den Fall eines falsch spezifizierten Modells führen wir eine spezielle Stufenfunktion ein und weisen eine punktweise Fehlerschranke im Vergleich zum Schätzer des Algorithmus nach. Des Weiteren entwickeln wir eine neue Methode zur Entrauschung von diffusionsgewichteten Magnetresonanzdaten. Unser neues Verfahren (ms)POAS basiert auf einer speziellen Beschreibung der Daten, die eine zeitgleiche Glättung bezüglich der gemessenen Positionen und der Richtungen der verwendeten Diffusionsgradienten ermöglicht. Für den kombinierten Messraum schlagen wir zwei Distanzfunktionen vor, deren Eignung wir mithilfe eines differentialgeometrischen Ansatzes nachweisen. Schließlich demonstrieren wir das große Potential von (ms)POAS auf simulierten und experimentellen Daten. / In statistics, nonparametric estimation is often based on local parametric modeling. For pointwise estimation of the target function, the parametric neighborhoods can be described by weights that depend on design points or on observations. As it turned out, the comparison of noisy observations at single points suffers from a lack of robustness. The Propagation-Separation Approach by Polzehl and Spokoiny [2006] overcomes this problem by using a multiscale approach with iteratively updated weights. The method has been successfully applied to a large variety of statistical problems. Here, we present a theoretical study and numerical results, which provide a better understanding of this versatile procedure. For this purpose, we introduce and analyse a novel strategy for the choice of the crucial parameter of the algorithm, namely the adaptation bandwidth. In particular, we study its variability with respect to the unknown target function. This justifies a choice independent of the data at hand. For piecewise constant and piecewise bounded functions, this choice enables theoretical proofs of the main heuristic properties of the algorithm. Additionally, we consider the case of a misspecified model. Here, we introduce a specific step function, and we establish a pointwise error bound between this function and the corresponding estimates of the Propagation-Separation Approach. Finally, we develop a method for the denoising of diffusion-weighted magnetic resonance data, which is based on the Propagation-Separation Approach. Our new procedure, called (ms)POAS, relies on a specific description of the data, which enables simultaneous smoothing in the measured positions and with respect to the directions of the applied diffusion-weighting magnetic field gradients. We define and justify two distance functions on the combined measurement space, where we follow a differential geometric approach. We demonstrate the capability of (ms)POAS on simulated and experimental data.

A pesquisa procurou levantar a relação entre concentração acionária e risco de expropriação de riqueza dos credores no Brasil. O universo amostral compreendeu as empresas de capital aberto listadas na Bovespa no período de 1997 a 2011. Foram traçados dois objetivos na pesquisa: (i) verificar se empresas com a presença de controle acionário definido apresentam maior percepção de risco de expropriação de riqueza dos credores do que aquelas que não apresentam concentração acionária; e (ii) verificar entre as empresas com a presença de controle acionário definido se maior participação no controle gera maior percepção de risco de expropriação de riqueza de terceiros. O suporte teórico do trabalho se deu em estudos sobre estrutura de capital, controle de capital, mercado de crédito e custo de capital de terceiros no Brasil. As variáveis estudadas foram o percentual de ações ON pelos principais acionistas e o custo da dívida medido pelo Ki. Os procedimentos estatísticos se deram pelos testes não paramétricos U de Man-Whitney e Kruskal-Wallis com comparações múltiplas entre grupos. A primeira resposta apresentou indícios, com significância estatística de 5%, que empresas com controle acionário definido tendem a apresentar maior risco de expropriação de riqueza de terceiros do que as demais. Entretanto, quando o controle é exercido por um único acionista que possui 50% ou mais das ações com direito a voto, as empresas tendem a apresentar menor risco de expropriação de riqueza dos credores do que as demais. A segunda resposta encontrada, também com significância estatística de 5%, apontou que, em empresas com a presença de um único acionista na posse de 50% ou mais das ações ON, à medida que esse principal acionista aumenta a participação no controle, o custo da dívida, variável explicativa de risco de expropriação de riqueza de terceiros, tende a diminuir. Portanto, acredita-se que o presente estudo cumpre a proposta de investigação apresentada ao não encontrar evidências que permitam descartar a ideia de que existe relação entre controle acionário definido e risco de expropriação de riqueza dos credores.Palavras-chave: Apreçamento de opções, Modelo HJM Gaussiano, Regressão não paramétrica. / The survey tried to raise the relationship between ownership concentration and risk of expropriation of creditors\' wealth in Brazil. The sample universe consisted of publicly traded companies listed on Bovespa in the period 1997-2011. Two main objectives were outlined: (i) verify if companies with the presence of defined shareholder control have a higher perception of risk of expropriation of creditors\' wealth than those who do not have shareholder control, and (ii) check between companies with defined shareholder control set if greater participation in the control creates higher perception of risk of expropriation of third parties\' wealth. The theoretical basis of the work was in studies on capital structure, capital controls, credit market and cost of third party capital in Brazil. The variables studied were the percentage of ON shares by principal shareholders and the cost of debt measured by Ki. Statistical procedures were given by nonparametric tests U of Mann Whitney and Kruskal-Wallis with multiple comparisons between groups. The first response, with statistical significance of 5%, showed that companies with defined shareholder control set tend to have a higher risk of expropriation of third parties\' wealth than others. However, when the control is exercised by a single shareholder who holds 50% or more of voting shares, companies tend to have lower risk of expropriation of creditors\' wealth than others. The second one, also with a statistical significance of 5%, pointed out that in companies with a single shareholder who holds 50% or more of ON shares, as this principal shareholder increases his participation in the control, the cost of debt, explanatory variable risk of expropriation of third parties\' wealth, tends to decrease. Therefore, it is believed that this study fulfils the investigation proposal presented to find no evidence to discard the idea that there is a relationship between defined shareholder control and risk of expropriation of creditors\' wealth.