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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Estimating the Local False Discovery Rate via a Bootstrap Solution to the Reference Class Problem: Application to Genetic Association Data

Abbas Aghababazadeh, Farnoosh January 2015 (has links)
Modern scientific technology such as microarrays, imaging devices, genome-wide association studies or social science surveys provide statisticians with hundreds or even thousands of tests to consider simultaneously. Testing many thousands of null hypotheses may increase the number of Type $I$ errors. In large-scale hypothesis testing, researchers can use different statistical techniques such as family-wise error rates, false discovery rates, permutation methods, local false discovery rate, where all available data usually should be analyzed together. In applications, the thousands of tests are related by a scientifically meaningful structure. Ignoring that structure can be misleading as it may increase the number of false positives and false negatives. As an example, in genome-wide association studies each test corresponds to a specific genetic marker. In such a case, the scientific structure for each genetic marker can be its minor allele frequency. In this research, the local false discovery rate as a relevant statistical approach is considered to analyze the thousands of tests together. We present a model for multiple hypothesis testing when the scientific structure of each test is incorporated as a co-variate. The purpose of this model is to incorporate the co-variate to improve the performance of testing procedures. The method we consider has different estimates depending on the tuning parameter. We would like to estimate the optimal value of that parameter by considering observed statistics. Thus, among those estimators, the one which minimizes the estimated errors due to bias and to variance is chosen by applying the bootstrap approach. Such an estimation method is called an adaptive reference class method. Under the combined reference class method, the effect of the co-variates is ignored and all null hypotheses should be analyzed together. In this research, under some assumptions for the co-variates and the prior probabilities, the proposed adaptive reference class method shows smaller error than the combined reference class method in estimating the local false discovery rate, when the number of tests gets large. We describe the adaptive reference class method to the coronary artery disease data, and we use simulation data to evaluate the performance of the estimator associated with the adaptive reference class method.
2

Méthodes de rééchantillonnage en méthodologie d'enquête

Mashreghi, Zeinab 10 1900 (has links)
Le sujet principal de cette thèse porte sur l'étude de l'estimation de la variance d'une statistique basée sur des données d'enquête imputées via le bootstrap (ou la méthode de Cyrano). L'application d'une méthode bootstrap conçue pour des données d'enquête complètes (en absence de non-réponse) en présence de valeurs imputées et faire comme si celles-ci étaient de vraies observations peut conduire à une sous-estimation de la variance. Dans ce contexte, Shao et Sitter (1996) ont introduit une procédure bootstrap dans laquelle la variable étudiée et l'indicateur de réponse sont rééchantillonnés ensemble et les non-répondants bootstrap sont imputés de la même manière qu'est traité l'échantillon original. L'estimation bootstrap de la variance obtenue est valide lorsque la fraction de sondage est faible. Dans le chapitre 1, nous commençons par faire une revue des méthodes bootstrap existantes pour les données d'enquête (complètes et imputées) et les présentons dans un cadre unifié pour la première fois dans la littérature. Dans le chapitre 2, nous introduisons une nouvelle procédure bootstrap pour estimer la variance sous l'approche du modèle de non-réponse lorsque le mécanisme de non-réponse uniforme est présumé. En utilisant seulement les informations sur le taux de réponse, contrairement à Shao et Sitter (1996) qui nécessite l'indicateur de réponse individuelle, l'indicateur de réponse bootstrap est généré pour chaque échantillon bootstrap menant à un estimateur bootstrap de la variance valide même pour les fractions de sondage non-négligeables. Dans le chapitre 3, nous étudions les approches bootstrap par pseudo-population et nous considérons une classe plus générale de mécanismes de non-réponse. Nous développons deux procédures bootstrap par pseudo-population pour estimer la variance d'un estimateur imputé par rapport à l'approche du modèle de non-réponse et à celle du modèle d'imputation. Ces procédures sont également valides même pour des fractions de sondage non-négligeables. / The aim of this thesis is to study the bootstrap variance estimators of a statistic based on imputed survey data. Applying a bootstrap method designed for complete survey data (full response) in the presence of imputed values and treating them as true observations may lead to underestimation of the variance. In this context, Shao and Sitter (1996) introduced a bootstrap procedure in which the variable under study and the response status are bootstrapped together and bootstrap non-respondents are imputed using the imputation method applied on the original sample. The resulting bootstrap variance estimator is valid when the sampling fraction is small. In Chapter 1, we begin by doing a survey of the existing bootstrap methods for (complete and imputed) survey data and, for the first time in the literature, present them in a unified framework. In Chapter 2, we introduce a new bootstrap procedure to estimate the variance under the non-response model approach when the uniform non-response mechanism is assumed. Using only information about the response rate, unlike Shao and Sitter (1996) which requires the individual response status, the bootstrap response status is generated for each selected bootstrap sample leading to a valid bootstrap variance estimator even for non-negligible sampling fractions. In Chapter 3, we investigate pseudo-population bootstrap approaches and we consider a more general class of non-response mechanisms. We develop two pseudo-population bootstrap procedures to estimate the variance of an imputed estimator with respect to the non-response model and the imputation model approaches. These procedures are also valid even for non-negligible sampling fractions.

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