No description available.

Thesis (Ph. D.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 169-173). Also available in print.

Berlin, Freie Univ., Diss., 2003. / Dateiforamt: zip, Dateien im PDF-Format. Computerdatei im Fernzugriff.

Berlin, Freie Universiẗat, Diss., 2003. / Dateiforamt: zip, Dateien im PDF-Format.

Purdue University West Lafayette (PUWL) / For massive data analysis, the computational bottlenecks exist in two ways. Firstly, the data could be too large that it is not easy to store and read. Secondly, the computation time could be too long. To tackle these problems, parallel computing algorithms like Divide-and-Conquer were proposed, while one of its drawbacks is that some correlations may be lost when the data is divided into chunks. Subsampling is another way to simultaneously solve the problems of the massive data analysis while taking correlation into consideration. The uniform sampling is simple and fast, but it is inefficient, see detailed discussions in Mahoney (2011) and Peng and Tan (2018). The bootstrap approach uses uniform sampling and is computing time in- tensive, which will be enormously challenged when data size is massive. k-means clustering is standard method in data analysis. This method does iterations to find centroids, which would encounter difficulty when data size is massive. In this thesis, we propose the approach of optimal subsampling for massive data bootstrapping and massive data k-means clustering. We seek the sampling distribution which minimize the trace of the variance co-variance matrix of the resulting subsampling estimators. This is referred to as A-optimal in the literature. We define the optimal sampling distribution by minimizing the sum of the component variances of the subsampling estimators. We show the subsampling k-means centroids consistently approximates the full data centroids, and prove the asymptotic normality using the empirical pro- cess theory. We perform extensive simulation to evaluate the numerical performance of the proposed optimal subsampling approach through the empirical MSE and the running times. We also applied the subsampling approach to real data. For massive data bootstrap, we conducted a large simulation study in the framework of the linear regression based on the A-optimal theory proposed by Peng and Tan (2018). We focus on the performance of confidence intervals computed from A-optimal sub- sampling, including coverage probabilities, interval lengths and running times. In both bootstrap and clustering we compared the A-optimal subsampling with uniform subsampling.

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Thesis advisor: Hao Wu / Thesis advisor: Ehri Ryu / In SEM, fit indexes provide useful information about how well a hypothesized model fits the population. Bootstrap has been applied to construct confidence internals for fit indexes. We proposed the most recent method for constructing confidence intervals (CIs) of fit indexes (Cheng & Wu, 2017): the bootstrap-test-based method. This dissertation includes the most popular bootstrap CI methods and the bootstrap-test-based method. In addition to the percentile bootstrap CI method used in Zhang and Savalei (2016), we also included other popular bootstrap CI methods. For all bootstrap CI methods, we explored their performances with and without the transformation proposed by Yuan, Hayashi, and Yanagihara (2007). In this process, we also solved computation difficulty for Studentized CI. The bootstrap-test-based method is improved by using alternative search statistics. As the previous approaches were not extended to nonnormal conditions, the CI estimation for fit indexes with nonnormal data are investigated for both bootstrap CI and bootstrap-test-based methods, using adjusted definitions of fit indexes for nonnormal data. Different nonnormal data generation techniques are applied. This dissertation presents a comprehensive comparison of bootstrap CI methods and the bootstrap-test-based method under various conditions. From the simulation results, the CIs for fit indexes under the bootstrap-test-based method are more accurate than most bootstrap CI methods. The results also show that the bootstrap-test-based method can be generalized well to non-normal data. The confidence bounds coverage by bootstrap-test-based method are closer to their nominal levels. / Thesis (PhD) — Boston College, 2021. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Psychology.

The efficacies of two anti-inflammatory drugs in ankylosing spondylitis and related complaints were studied at a single medical clinic over a period of twenty-eight weeks. The purposes of this project were: (1) -To determine .any significant differences within and between the two drug groups using well-known nonparametric procedures, and (2) To illustrate the use of the bootstrap method and determine whether it is appropriate and useful for this data set. Some statistically significant changes indicative of improvement occurred among both groups of patients for primary efficacy variables. No definite trend was found for most of the laboratory variables. Both drugs demonstrated effective pain relief. Regarding the variables of day and night pain relief as well as pulse, the Experimental Drug proved to be clinically but not statistically superior to the other commonly used drug. Analyses of safety data indicated some statistically significant changes in both drug groups. There was a statistically significant difference between drug groups at baseline. / Thesis / Master of Science (MS)

Muitos estudos em diferentes áreas examinam como um conjunto de variáveis influencia algum tipo de percentagem, proporção ou frações. Modelos de regressão lineares não são satisfatórios para modelar tais dados. Uma classe de modelos de regressão beta que em muitos aspectos é semelhante aos modelos lineares generalizados foi proposto por Ferrari e Cribari--Neto~(2004). A resposta média é relacionada com um predictor linear por uma função de ligação e o predictor linear envolve covariáveis e parâmetros de regressão desconhecidos. O modelo também é indexado por um parâmetro de precisão. Smithson e Verkuilen,(2005), entre outros, consideram o modelo de regressão beta em que esse parâmetro varia ao longo das observações. Nesta tese foram desenvolvidas técnicas de diagnóstico para os modelos regressão beta com dispersão constante e com dispersão variável, sendo que o método e influência local (Cook,~1986) mostrou-se decisivo, inclusive no sentido de identificar dispersão variável nos dados. Adicionalmente, avaliamos através de estudos de simulação o desempenho de estimadores de máxima verossimilhança para o modelo de regressão beta com dispersão variável, as conseqüências de estimar o modelo supondo dispersão constante quando de fato ela é variável e de testes assintóticos para testar a hipótese de dispersão constante. Finalmente, utilizando um esquema de bootstrap (Davison e Hinkley,1997), desenvolvemos um procedimento de obtenção de limites de predição para o modelo de regressão com dispersão constante. Ilustramos a teoria desenvolvida com várias aplicações a dados reais. / Practitioners oftentimes wish to investigate how certain variables influence continuous variable that assumes values on the standard unit interval $(0,1)$, such as percentages, proportions, rates and fractions. Linear regression models are not suitable for modelling such data. A class of beta regression models which is in many aspects similar to that of generalised linear models was proposed by Ferrari and Cribari--Neto~(2004). The mean response is related to a linear predictor, which involves covariates and unknown regression parameters, through a link function. The model is also indexed by a precision parameter. Smithson e Verkuilen~(2005), among others, consider the beta regression model with variable dispersion, i.e., beta regression in which the precision parameter is not constant across observations. In this dissertation we develop diagnostic methods for beta regression models with both constant and variable dispersion. The method of local influence (Cook,~1986) proved to be particularly useful, since it is able to identify variable dispersion in the data. We have also used Monte Carlo simulation to evaluate the finite sample performance of maximum likelihood estimators in beta regression models with variable dispersion; we have also evaluated the consequences os misspecifying the model by incorrectly assuming constant dispersion when dispersion is variable and the finite sample behavior of heteroskedasticity tests based on first order asymptotics. of estimating the model supposing constant dispersion when Prediction bootstrap intervals (Davison e Hinkley,~1997) for the beta regression model with constant dispersion are also considered.Practical applications that employ real data are presented and discussed.

Muitos estudos em diferentes áreas examinam como um conjunto de variáveis influencia algum tipo de percentagem, proporção ou frações. Modelos de regressão lineares não são satisfatórios para modelar tais dados. Uma classe de modelos de regressão beta que em muitos aspectos é semelhante aos modelos lineares generalizados foi proposto por Ferrari e Cribari--Neto~(2004). A resposta média é relacionada com um predictor linear por uma função de ligação e o predictor linear envolve covariáveis e parâmetros de regressão desconhecidos. O modelo também é indexado por um parâmetro de precisão. Smithson e Verkuilen,(2005), entre outros, consideram o modelo de regressão beta em que esse parâmetro varia ao longo das observações. Nesta tese foram desenvolvidas técnicas de diagnóstico para os modelos regressão beta com dispersão constante e com dispersão variável, sendo que o método e influência local (Cook,~1986) mostrou-se decisivo, inclusive no sentido de identificar dispersão variável nos dados. Adicionalmente, avaliamos através de estudos de simulação o desempenho de estimadores de máxima verossimilhança para o modelo de regressão beta com dispersão variável, as conseqüências de estimar o modelo supondo dispersão constante quando de fato ela é variável e de testes assintóticos para testar a hipótese de dispersão constante. Finalmente, utilizando um esquema de bootstrap (Davison e Hinkley,1997), desenvolvemos um procedimento de obtenção de limites de predição para o modelo de regressão com dispersão constante. Ilustramos a teoria desenvolvida com várias aplicações a dados reais. / Practitioners oftentimes wish to investigate how certain variables influence continuous variable that assumes values on the standard unit interval $(0,1)$, such as percentages, proportions, rates and fractions. Linear regression models are not suitable for modelling such data. A class of beta regression models which is in many aspects similar to that of generalised linear models was proposed by Ferrari and Cribari--Neto~(2004). The mean response is related to a linear predictor, which involves covariates and unknown regression parameters, through a link function. The model is also indexed by a precision parameter. Smithson e Verkuilen~(2005), among others, consider the beta regression model with variable dispersion, i.e., beta regression in which the precision parameter is not constant across observations. In this dissertation we develop diagnostic methods for beta regression models with both constant and variable dispersion. The method of local influence (Cook,~1986) proved to be particularly useful, since it is able to identify variable dispersion in the data. We have also used Monte Carlo simulation to evaluate the finite sample performance of maximum likelihood estimators in beta regression models with variable dispersion; we have also evaluated the consequences os misspecifying the model by incorrectly assuming constant dispersion when dispersion is variable and the finite sample behavior of heteroskedasticity tests based on first order asymptotics. of estimating the model supposing constant dispersion when Prediction bootstrap intervals (Davison e Hinkley,~1997) for the beta regression model with constant dispersion are also considered.Practical applications that employ real data are presented and discussed.