Orientador: Nancy Lopes Garcia / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-11T16:45:43Z (GMT). No. of bitstreams: 1 Goto_DanielaBentoFonsechi_M.pdf: 3513260 bytes, checksum: ff6f9e35005ad9015007d1f51ee722c1 (MD5) Previous issue date: 2008 / Resumo: O objetivo desta dissertação é estudar estimação de máxima verossimilhança para processos de nascimento puro espacial para dois diferentes tipos de amostragem: a) quando há observação permanente em um intervalo [0, T]; b) quando o processo é observado após um tempo T fixo. No caso b) não se conhece o tempo de nascimento dos pontos, somente sua localização (dados faltantes). A função de verossimilhança pode ser escrita para o processo de nascimento puro não homogêneo em um conjunto compacto através do método da projeção descrito por Garcia and Kurtz (2008), como projeção da função de verossimilhança. A verossimilhança projetada pode ser interpretada como uma esperança e métodos de Monte Carlo podem ser utilizados para estimar os parâmetros. Resultados sobre convergência quase-certa e em distribuição são obtidos para a aproximação do estimador de máxima verossimilhança. Estudos de simulação mostram que as aproximações são adequadas. / Abstract: The goal of this work is to study the maximum likelihood estimation of a spatial pure birth process under two different sampling schemes: a) permanent observation in a fixed time interval [0, T]; b) observation of the process only after a fixed time T. Under scheme b) we don't know the birth times, we have a problem of missing variables. We can write the likelihood function for the nonhomogeneous pure birth process on a compact set through the method of projection described by Garcia and Kurtz (2008), as the projection of the likelihood function. The fact that the projected likelihood can be interpreted as an expectation suggests that Monte Carlo methods can be used to compute estimators. Results of convergence almost surely and in distribution are obtained for the aproximants to the maximum likelihood estimator. Simulation studies show that the approximants are appropriate. / Mestrado / Inferencia em Processos Estocasticos / Mestre em Estatística

[pt] Geralmente, em análises estatísticas, dados faltantes em ao menos uma variável resulta da completa eliminação da unidade respondente. Esta estratégia, padrão na maioria dos pacotes estatísticos, não produz resultados livres de viés, a não ser que os dados faltantes sejam Missing Completly At Random (MCAR). A tese mostra a classificação usada para o mecanismo gerador de dados faltantes e a modelagem de dados categóricos levando em conta os dados faltantes. Para isto, utiliza-se o modelo loglinear em combinação com o algoritmo EM (Expectation-Maximization). Esta combinação produz o algoritmo conhecido como ECM (Expectation-Conditional Maximization). A aplicação do método é feita com os dados do SAEB (Sistema Nacional de Avaliação da Educação Básica) para o ano de 1999, investigando a relação entre o responsável pelo desenvolvimento do projeto pedagógico na escola e o impacto na proficiência média da escola. / [en] Generally, in statiscal analysis, missing value in one variable at least, implies the elimination of the respondent unit. That strategy, default in the most of statistical softwares, don´t produce results free from bias, unless the missing data are Missing Completly At Random (MCAR). This dissertation shows the classification about the mechanisms that lead to missing data and the modeling of categorical data dealing with missing data. To do that we combine loglinear model and the EM (Expectation-Maximization)algorithm. This combination produce the agorithm called ECM (Expectation-Conditional Maximization) algorithm. The method is applied to SAEB educational data. The objective is to investigate the relationship between responsable for developing the pedagogic project and the impact on the mean proficiency of school.

Philosophiae Doctor - PhD / Missing data are common in survey data sets. Enrolled subjects do not often have data recorded for all variables of interest. The inappropriate handling of missing data may lead to bias in the estimates and incorrect inferences. Therefore, special attention is needed when analysing incomplete data. The multivariate normal imputation (MVNI) and the multiple imputation by chained equations (MICE) have emerged as the best techniques to impute or fills in missing data. The former assumes a normal distribution of the variables in the imputation model, but can also handle missing data whose distributions are not normal. The latter fills in missing values taking into account the distributional form of the variables to be imputed. The aim of this study was to determine the performance of these methods when data are missing at random (MAR) or completely at random (MCAR) on unordered or nominal categorical variables treated as predictors or response variables in the regression models. Both dichotomous and polytomous variables were considered in the analysis. The baseline data used was the 2007 Demographic and Health Survey (DHS) from the Democratic Republic of Congo. The analysis model of interest was the logistic regression model of the woman’s contraceptive method use status on her marital status, controlling or not for other covariates (continuous, nominal and ordinal). Based on the data set with missing values, data sets with missing at random and missing completely at random observations on either the covariates or response variables measured on nominal scale were first simulated, and then used for imputation purposes. Under MVNI method, unordered categorical variables were first dichotomised, and then K − 1 (where K is the number of levels of the categorical variable of interest) dichotomised variables were included in the imputation model, leaving the other category as a reference. These variables were imputed as continuous variables using a linear regression model. Imputation with MICE considered the distributional form of each variable to be imputed. That is, imputations were drawn using binary and multinomial logistic regressions for dichotomous and polytomous variables respectively. The performance of these methods was evaluated in terms of bias and standard errors in regression coefficients that were estimated to determine the association between the woman’s contraceptive methods use status and her marital status, controlling or not for other types of variables. The analysis was done assuming that the sample was not weighted fi then the sample weight was taken into account to assess whether the sample design would affect the performance of the multiple imputation methods of interest, namely MVNI and MICE. As expected, the results showed that for all the models, MVNI and MICE produced less biased smaller standard errors than the case deletion (CD) method, which discards items with missing values from the analysis. Moreover, it was found that when data were missing (MCAR or MAR) on the nominal variables that were treated as predictors in the regression model, MVNI reduced bias in the regression coefficients and standard errors compared to MICE, for both unweighted and weighted data sets. On the other hand, the results indicated that MICE outperforms MVNI when data were missing on the response variables, either the binary or polytomous. Furthermore, it was noted that the sample design (sample weights), the rates of missingness and the missing data mechanisms (MCAR or MAR) did not affect the behaviour of the multiple imputation methods that were considered in this study. Thus, based on these results, it can be concluded that when missing values are present on the outcome variables measured on a nominal scale in regression models, the distributional form of the variable with missing values should be taken into account. When these variables are used as predictors (with missing observations), the parametric imputation approach (MVNI) would be a better option than MICE.

This dissertation provides three novel methodologies to the field of political science. In the first chapter, I describe how to make causal inferences in the face of dynamic strategies. Traditional causal inference methods assume that these dynamic decisions are made all at once, an assumption that forces a choice between omitted variable bias and post-treatment bias. I resolve this dilemma by adapting methods from biostatistics and use these methods to estimate the effectiveness of an inherently dynamic process: a candidate's decision to "go negative." Drawing on U.S. statewide elections (2000-2006), I find, in contrast to the previous literature, that negative advertising is an effective strategy for non-incumbents. In the second chapter, I develop a method for handling measurement error. Social scientists devote considerable effort to mitigating measurement error during data collection but then ignore the issue during analysis. Although many statistical methods have been proposed for reducing measurement error-induced biases, few have been widely used because implausible assumptions, high levels of model dependence, difficult computation, or inapplicability with multiple mismeasured variables. This chapter develops an easy-to-use alternative without these problems as a special case of extreme measurement error and corrects for both. In the final chapter, I introduce a model for detecting changepoints in the distribution of contributions data because it allows for overdispersion, a key feature of contributions data. While many extant changepoint models force researchers to choose the number of changepoint ex ante, the game-changers model incorporates a Dirichlet process prior in order to estimate the number of changepoints along with their location. I demonstrate the usefulness of the model in data from the 2012 Republican primary and the 2008 U.S. Senate elections. / Government

Mendelian randomization is an epidemiological method for using genetic variationto estimate the causal effect of the change in a modifiable phenotype onan outcome from observational data. A genetic variant satisfying the assumptionsof an instrumental variable for the phenotype of interest can be usedto divide a population into subgroups which differ systematically only in thephenotype. This gives a causal estimate which is asymptotically free of biasfrom confounding and reverse causation. However, the variance of the causalestimate is large compared to traditional regression methods, requiring largeamounts of data and necessitating methods for efficient data synthesis. Additionally,if the association between the genetic variant and the phenotype is notstrong, then the causal estimates will be biased due to the “weak instrument”in finite samples in the direction of the observational association. This biasmay convince a researcher that an observed association is causal. If the causalparameter estimated is an odds ratio, then the parameter of association willdiffer depending on whether viewed as a population-averaged causal effect ora personal causal effect conditional on covariates. We introduce a Bayesian framework for instrumental variable analysis, whichis less susceptible to weak instrument bias than traditional two-stage methods,has correct coverage with weak instruments, and is able to efficiently combinegene–phenotype–outcome data from multiple heterogeneous sources. Methodsfor imputing missing genetic data are developed, allowing multiple genetic variantsto be used without reduction in sample size. We focus on the question ofa binary outcome, illustrating how the collapsing of the odds ratio over heterogeneousstrata in the population means that the two-stage and the Bayesianmethods estimate a population-averaged marginal causal effect similar to thatestimated by a randomized trial, but which typically differs from the conditionaleffect estimated by standard regression methods. We show how thesemethods can be adjusted to give an estimate closer to the conditional effect. We apply the methods and techniques discussed to data on the causal effect ofC-reactive protein on fibrinogen and coronary heart disease, concluding withan overall estimate of causal association based on the totality of available datafrom 42 studies.

La problématique de la gestion des données manquantes dans les études épidémiologiques est un sujet qui intéressera tous les chercheurs impliqués dans l’analyse des données recueillies et dans l’interprétation des résultats issus de ces analyses. Et même si la question de la gestion des données manquantes et de leur impact sur la validité des résultats obtenus est souvent discutée, cesont souvent les méthodes de traitement des données manquantes les plus simples mais pas toujours les plus valides qui sont utilisées en pratique. L’utilisation de chacune de ces méthodes suppose un certain nombre d’hypothèses sous lesquelles les résultats obtenus sont valides, mais il n’est pas toujours possible de tester ces hypothèses. L’objectif de ce travail était (i) de proposer une revue des différentes méthodes de traitement des données manquantes utilisées en épidémiologie en discutant les avantages et les limites de chacune de ces méthodes, (ii) de proposer une stratégie d’analyse afin d’étudier la robustesse des résultats obtenues via les méthodes classiques de traitement des données manquantes à l’écart aux hypothèses qui, bien que non testables, sont nécessaires à la validité de ces résultats, et (iii) de proposer quelques applications sur des données réelles des différents point discutés dans les deux premières parties. / The issue of how to deal with missing data in epidemiological studies is a topic which concerns every researcher involved in the analysis of collected data and in the interpretation of the results produced by these analyses. And even if the issue of the handling of missing data and of their impact on the validity of the results is often discussed, simple, but not always appropriate methods to deal with missing data are commonly used. The use of each of these methods is based on some hypotheses under which the obtained results are valid, but it is not always possible to test these hypotheses. The objective of this work was (i) to propose a review of various methods to handle missing data used in the field of epidemiology, and to discuss the advantages and disadvantages of each of these methods, (ii) to propose a strategy of analysis in order to study the robustness of the results obtained via classical methods to handle missing data to the departure from hypotheses which are required for the validity of these results, although they are not testable, and (iii) to propose some applications on real data of the issues discussed in the first two sections.

Multivariate normal distribution is commonly encountered in any field, a frequent issue is the missing values in practice. The purpose of this research was to estimate the parameters in three-dimensional covariance permutation-symmetric normal distribution with complete data and all possible patterns of incomplete data. In this study, MLE with missing data were derived, and the properties of the MLE as well as the sampling distributions were obtained. A Monte Carlo simulation study was used to evaluate the performance of the considered estimators for both cases when ρ was known and unknown. All results indicated that, compared to estimators in the case of omitting observations with missing data, the estimators derived in this article led to better performance. Furthermore, when ρ was unknown, using the estimate of ρ would lead to the same conclusion.

The Diploma thesis deals with reconstruction of Missing data of an Image. It is done by the use of appropriate Mathematical theory and numerical algorithm to reconstruct missing information. The result of this implementation is the reconstruction of missing image information. The thesis also compares different numerical methods, and see which one of them perform best in terms of efficiency and accuracy of the given problem, hence it is used for the reconstruction of missing data.

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