Orientadores: Veronica Andrea Gonzales-Lopez, Laura Leticia Ramos Rifo / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-07T14:24:13Z (GMT). No. of bitstreams: 1 Viola_MarcioLuisLanfredi_M.pdf: 24648946 bytes, checksum: 3e9e740e3961441870b59a758583d5af (MD5) Previous issue date: 2006 / Resumo: Sob a ótica da Teoria de Cópulas, a modelagem multidimensional pode ser considerada decorrente de dois processos: estimação das funções de distribuição acumulada marginais e modelagem de uma estrutura de dependência multidimensional que age sobre tais funções de distribuição marginais, sendo esta última, denominada cópula. Neste trabalho, as funções de distribuição acumulada marginais de interesse correspondem à função de distribuição acumulada do máximo de uma variável aleatória e, consequentemente, a Teoria de Valores Extremos apresenta-se como uma alternativa natural para a modelagem das distribuições marginais. Nesta dissertação, serão estudados os tipos de dependência entre variáveis aleatórias, a construção e implementação de modelos de Teoria de Cópulas assim como, os resultados básicos de convergência utilizados na Teoria de Valores Extremos. Sob o escopo da Teoria de Valores Extremos, os métodos de estimação pontual de Máxima Verossimilhança e L-momentos serão comparados através de algumas simulações e, adicionalmente, serão abordadas as condições que asseguram a validade das propriedades assintóticas do Método de Máxima Verossimilhança bem como as principais propriedades de ambos os métodos citados. As teorias citadas serão aplicadas no contexto de Lingüística na modelagem multidimensional de características do sinal acústico observadas em regiões de baixa, média e alta freqüência de frases das línguas inglesa e francesa / Abstract: In the copula theory we can interpret a multidimensional distribution as a result of two processes, namely, marginal cumulative distribution function estimation and dependence structure estimation. The latter, called copula, is employed to aggregate the marginal distributions. In this work, the marginal distributions correspond to the maximum value of random variables. Thus, the extreme value theory, in particular the generalized extreme value distribution, is a natural way to model the marginal distribution. Some theoretical aspects will be studied in order to obtain knowledge the principal results of concerning the convergence in distribution associated with maximum likelihood estimation and L-moments estimation. This strategy is essential because the generalized extreme value distribution represents a nonregular case. Some simulation were performed in order to compare the behavior of the method. We will also take into account trivariate copula models such as Kimeldorf and Sampson model and Gumbel model. We will use maximum likelihood method for the point estimation in copula models. Finally, we will apply extreme value theory and copula model in a linguistic problem. Preciselly, we will consider signal coming from the three different frequence classes modeled both English and French languages / Mestrado / Mestre em Estatística

Orientador: Laura Leticia Ramos Rifo / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T10:19:46Z (GMT). No. of bitstreams: 1 Coura_AndredaSilva_M.pdf: 8253159 bytes, checksum: 4cf2d4abd8227260acd62a6dd9dc2b98 (MD5) Previous issue date: 2014 / Resumo: A dissertação apresenta uma abordagem prática para o ensino da matemática nos níveis fundamental e médio. De forma mais específica, apresenta conceitos de estatística básica como tratamento de informações e estudo de probabilidades. Estes conceitos são de grande importância no âmbito científico (parte experimental, por exemplo) e social (compreensão de características populacionais), além de estarem inseridos na vida cotidiana dos alunos. Sendo assim, foi entendido que é primordial desenvolver as competências e habilidades para organizar e compreender informações. Foram realizados experimentos para a aplicação dos conceitos apresentados em sala de aula. Também uma pesquisa propondo questões para analisar aspectos sobre alimentação e prática de exercícios físicos. Estes experimentos, além da aplicação dos conceitos, pretendem desenvolver no público-alvo, raciocínio lógico e olhar crítico, para assuntos relacionados à disciplina de matemática, utilizando situações cotidianas. Para análise organizamos e interpretamos as informações por meio de tabelas e gráficos. A pesquisa teve como objetivo principal mostrar como é usada a teoria estatística para a tomada de decisão e, nesse caso, para melhorar a própria qualidade de vida. Desse modo, pretendemos que a metodologia apresentada neste trabalho possa contribuir para a disseminação do conhecimento destas ferramentas matemáticas para os níveis fundamental e médio do ensino escolar / Abstract: This dissertation presents a practical approach for teaching mathematics in the elementary and secondary levels. More specifically, presents concepts of Basic Statistics as information processing and the study of probabilities. These concepts are of great importance in scientific (experimental way, for example) and social (understanding of population characteristics), besides being inserted into the daily student's lives. Therefore, it was understood that is necessary to develop the skills and abilities to organize and understand information. Experiments were carried out for the application of the concepts presented in classroom. Also a search posing questions to analyze aspects of food and physical exercise. The realization of these experiments purpose, besides the application of classroom learnt concepts, develop in students, logic reasoning and critical look at issues related to the discipline of mathematics and daily situations by organizing and interpreting information with charts and graphs. The research aimed to show how it is used statistical theory for decision making and, if so , to improve their quality of life. Thus, we intend that presented methodology in this study may contribute to the dissemination of these mathematical knowledge tools for elementary and high school levels / Mestrado / Matemática em Rede Nacional / Mestre em Matemática em Rede Nacional

Orientador: Maria Cristina de Castro Cunha / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T19:33:01Z (GMT). No. of bitstreams: 1 Campos_FabioAntonioAraujode_D.pdf: 1374668 bytes, checksum: 6318414d486cf4810705b84e0d722e77 (MD5) Previous issue date: 2015 / Resumo: Neste trabalho estudamos o sistema de equações diferenciais estocásticas obtido na linearização do modelo de propagação de ondas acústicas. Mais especificamente, analisamos métodos para solução do sistema de equações diferenciais usado na acústica linear, onde a matriz com dados aleatórios e um vetor de funções aleatórias que define as condições iniciais. Além do tradicional Método de Monte Carlo aplicamos o Método de Transformações de Variáveis Aleatórias e o Método de Galerkin Estocástico. Apresentamos resultados obtidos usando diferentes distribuições de probabilidades dos dados do problema. Também comparamos os métodos através da distribuição de probabilidade e momentos estatísticos da solução / Abstract: On the present work we study the system of stochastic differential equations obtained from the linearization of the propagation model of acoustic waves. More specifically we analyze methods for the solution of the system of differential equations used in the linear acoustics, where the matrix with random data and a vector of random functions defining initial conditions. In addition to the traditional Monte Carlo Method we apply the Variable Transformations of Random Method and the Galerkin Stochastic Method. We present results obtained using different probability distributions of problem data. We also compared the methods through the distribution of probabilities and statistical moments of the solution / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

Advances in computing has undoubtfully been one of the main catalysts in the formation of the discipline always known as Statistics. A fundamental question addressed here is whether computing facilities, such as parallel or high performance computing, could assist in the development of methodologies that render stronger results, based on some predetermined optimality criterion. The candidate at the hand of which this enquiry is made, is the arc length of some statistical function. Estimation, goodness-of-fit, linear regression and non-linear regression, which may all be considered as central themes in Statistics, are revisited, and redefined in terms of this new measure. The results resulting from these arc length methodologies are obtained from simulation, as well as from real case studies, and contrasted to that obtained using their classical counterparts. Mathematical premises for the proposed methods are provided, together with the documentation accompanying the companion R package, along with the data utilised for the applications. / Thesis (PhD)--University of Pretoria, 2017. / National Research Foundation of South Africa, Unique Grant No. 94108. / Statistics / PhD / Unrestricted

Functional data analysis, commonly known as FDA", refers to the analysis of information on curves of functions. Key aspects of FDA include the choice of smoothing techniques, data reduction, model evaluation, functional linear modeling and forecasting methods. FDA is applicable in numerous applications such as Bioscience, Geology, Psychology, Sports Science, Econometrics, Meteorology, etc. This dissertation main objective is to focus more specifically on Functional Linear Regression Modelling (FLRM), which is an extension of Multivariate Linear Regression Modeling. The problem of constructing a Functional Linear Regression modelling with functional predictors and functional response variable is considered in great details. Discretely observed data for each variable involved in the modelling are expressed as smooth functions using: Fourier Basis, B-Splines Basis and Gaussian Basis. The Functional Linear Regression Model is estimated by the Least Square method, Maximum Likelihood method and more thoroughly by Penalized Maximum Likelihood method. A central issue when modelling Functional Regression models is the choice of a suitable model criterion as well as the number of basis functions and an appropriate smoothing parameter. Four different types of model criteria are reviewed: the Generalized Cross-Validation, the Generalized Information Criterion, the modified Akaike Information Criterion and Generalized Bayesian Information Criterion. Each of these aforementioned methods are applied to a dataset and contrasted based on their respective results.

This thesis studies two discrete optimization problems: ordering problems in optimal stopping theory and popular matchings. The main goal of this thesis is to find the boundary between NP-hardness and tractability for these problems, and whenever possible, designs polynomial-time algorithms for the easy cases and approximation schemes or prophet inequalities for the hard cases. In the first part of the thesis, we study ordering problems in optimal stopping theory. In the optimal stopping problem, a player is presented with 𝓃 random variables 𝑋₁, . . . , 𝑋n, whose distributions are known to the player, but not their realizations. After observing the realization of 𝑋ᵢ, the player can choose to stop and earn reward 𝑋ᵢ, or reject 𝑋ᵢ and probe the next variable 𝑋ᵢ₊₁. If 𝑋ᵢ is rejected, it cannot be accepted in the future. The goal of the player is to maximize the expected reward at stopping time. If the order of observation is fixed, the player can find the optimal stopping criteria using a dynamic program. In this thesis, we investigate the variant in which the player is able to choose the order of observation. What is the best ordering and what benefits does ordering bring? Chapter 2 introduces the optimal ordering problem in optimal stopping theory. We prove that the problem of finding an optimal ordering is NP-hard even in very restricted cases where the support of each distribution has support on at most three points. Next, we prove an FPTAS for the hardness case and provide a tractable algorithm and a prophet inequality for two-point distributions. Chapter 3 studies the optimal ordering problem when the player can choose 𝑘 > 1 rewards before stopping. We show that finding an optimal static ordering is NP-hard even for very simple two-point distributions. Next, we prove an FPTAS for the hardness case and give prophet inequalities under static and dynamic policies for two-point distributions. In the second part of the thesis, we study popular matchings. Suppose we are given a bipartite graph with independent sets 𝑨 and 𝐵. Each vertex in 𝑨 has a ranked order of preferences on the vertices in 𝐵, and vice versa. A matching 𝑴 is popular if for any other matching 𝑴′, the number of vertices that prefer 𝑴 is at least as much as the number of vertices that prefer 𝑴′. Chapter 4 studies popular matchings. In the first part, we provide a general reduction which, through minor adjustments, proves NP-Hardness for a variety of different questions, including that of finding a max-weight popular matching. In the second part, we restrict our attention to graphs of bounded treewidth and provide a tractable algorithm for finding a max-weight popular matching.

Many applied statistical applications face the potential problem of model contamination and measurement error. The form and degree of contamination as well as the measurement error are usually unknown and sample-specific, which brings additional challenges for researchers. In this thesis, we have proposed several Bayesian inference models to address these issues, with the application to one type of special data for allergen concentration measurement, which is called serial dilution data and is self-calibrated. In our first chapter, we address the problem of model contamination by using a multilevel model to simultaneously flag problematic observations and estimate unknown concentrations in serial dilution data, a problem where the current approach can lead to noisy estimates and difficulty in estimating very low or high concentrations. In our second chapter, we propose the Bayesian joint contamination model for modeling multiple measurement units at the same time while adjusting for differences between experiments using the idea of global calibration, and it could account for uncertainty in both predictors and response variables in Bayesian regression. We are able to get efficacy gain by analyzing multiple experiments together while maintaining robustness with the use of hierarchical models. In our third chapter, we develop a Bayesian two-step inference model to account for measurement uncertainty propagation in regression analysis when the joint inference model is infeasible. We aim to increase model inference reliability while providing flexibility to users by not restricting the type of inference model used in the first step. For each of the proposed methods, We also demonstrate how to integrate multiple model building blocks through the idea of Bayesian workflow. In extensive simulation studies, we show that our proposed methods outperform other commonly used approaches. For the data applications, we apply the proposed new methods to the New York City Neighborhood Asthma and Allergy Study (NYC NAAS) data to estimate indoor allergen concentrations more accurately as well as reveal the underlying associations between dust mite allergen concentrations and the exhaled nitric oxide (NO) measurement for asthmatic children. The methods and tools developed here have a wide range of applications and can be used to improve lab analyses, which are crucial for quantifying exposures to assess disease risk and evaluating interventions.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Civil Engineering, 1980 / Bibliography: leaves 441-455. / by Peter Douglas Hall. / Ph. D. / Ph. D. Massachusetts Institute of Technology, Department of Civil Engineering

Often the basic assumptions of the ANOVA for an experimental design are not met or the statistical model is incorrectly specified. Randomization of treatments to experimental units is expected to protect against such shortcomings. This paper uses randomization theory to examine the impact on the expectations of mean squares, treatment means, and treatment differences for two model mis·specifications: Systematic response shifts and correlated experimental units. Systematic response shifts are presented in the context of the randomized complete block design (RCBD). In particular fixed shifts are added to the responses of experimental units in the initial and final positions of each block. The fixed shifts are called border shifts. It is shown that the RCBD is an unbiased design under randomization theory when border shifts are present. Treatment means are biased but treatment differences are unbiased. However the estimate of error is biased upwards and the power of the F test is reduced. Alternative designs to the RCBD under border shifts are the Latin square, semi-Latin square, and two-column designs. Randomization analysis demonstrates that the Latin square is an unbiased design with an unbiased estimate of error and of treatment differences. The semi-Latin square has each of the t treatments occurring only once per row and column, but t is a multiple of the number of rows or columns. Thus each row-column combination contains more than one experimental unit. The semi-Latin square is a biased design with a biased estimate of error even when no border shifts are present. Row-column interaction is responsible for the bias. Border shifts do not contaminate the expected mean squares or treatment differences, and thus the semi-Latin square is a viable alternative when the border shift overwhelms the row-column interaction. The two columns of the two-column design correspond to the border and interior experimental units respectively. Results similar to that for the semi-Latin square are obtained. Simulation studies for the RCBD and its alternatives indicate that the power of the F test is reduced for the RCBD when border shifts are present. When no row-column interaction is present, the semi-Latin square and two-column designs provide good alternatives to the RCBD. Similar results are found for the split plot design when border shifts occur in the sub plots. A main effects plan is presented for situations when the number of whole plot units equals the number of sub plot units per whole plot. The analysis of designs in which the experimental units occur in a sequence and exhibit correlation is considered next. The Williams Type Il(a) design is examined in conjunction with the usual ANOVA and with the method of first differencing. Expected mean squares, treatment means, and treatment differences are obtained under randomization theory for each analysis. When only adjacent experimental units have non negligible correlation, the Type Il(a) design provides an unbiased error estimate for the usual ANOVA. However the expectation of the treatment mean square is biased downwards for a positive correlation. First differencing results in a biased test and a biased error estimate. The test is approximately unbiased if the correlation between units is close to a half. / Ph. D.

This study was an examination of the effect of type of correlation matrix on the robustness of LISREL maximum likelihood and unweighted least squares structural parameter estimates for models with categorical manifest variables. Two types of correlation matrices were analyzed; one containing Pearson product-moment correlations and one containing tetrachoric, polyserial, and product-moment correlations as appropriate. Using continuous variables generated according to the equations defining the population model, three cases were considered by dichotomizing some of the variables with varying degrees of skewness. When Pearson product-moment correlations were used to estimate associations involving dichotomous variables, the structural parameter estimates were biased when skewness was present in the dichotomous variables. Moreover, the degree of bias was consistent for both the maximum likelihood and unweighted least squares estimates. The standard errors of the estimates were found to be inflated, making significance tests unreliable. The analysis of mixed matrices produced average estimates that more closely approximated the model parameters except in the case where the dichotomous variables were skewed in opposite directions. However, since goodness-of-fit statistics and standard errors are not available in LISREL when tetrachoric and polyserial correlations are used, the unbiased estimates are not of practical significance. Until alternative computer programs are available that employ distribution-free estimation procedures that consider the skewness and kurtosis of the variables, researchers are ill-advised to employ LISREL in the estimation of structural equation models containing skewed categorical manifest variables. / Ph. D.