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Articles 1 - 9 of 9
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Jackknife Empirical Likelihood-Based Confidence Intervals For Low Income Proportions With Missing Data, Yanan Yin
Mathematics Theses
The estimation of low income proportions plays an important role in comparisons of poverty in different countries. In most countries, the stability of the society and the development of economics depend on the estimation of low income proportions. An accurate estimation of a low income proportion has a crucial role for the development of the natural economy and the improvement of people's living standards. In this thesis, the Jackknife empirical likelihood method is employed to construct confidence intervals for a low income proportion when the observed data had missing values. Comprehensive simulation studies are conducted to compare the relative performances …
Generalized Confidence Intervals For Partial Youden Index And Its Corresponding Optimal Cut-Off Point, Chenxue Li
Generalized Confidence Intervals For Partial Youden Index And Its Corresponding Optimal Cut-Off Point, Chenxue Li
Mathematics Theses
In the field of diagnostic test studies, the accuracy of a diagnostic test is essential in evaluating the performance of the test. The receiver operating characteristic (ROC) curve and the area under the curve (AUC) are widely used in such evaluation procedures. Meanwhile, the Youden index is also introduced into practice to measure the accuracy of the diagnostic test from another aspect. The Youden index maximizes the sum of sensitivity and specificity, assuring decent true positive and negative rates. It draws one's attention due to its merit of finding the optimal cut-off points of biomarkers. Similar to Partial ROC, a …
The Minimum Rank Of Sign Pattern Matrices With A 1-Separation, Wenyan Zhou
The Minimum Rank Of Sign Pattern Matrices With A 1-Separation, Wenyan Zhou
Mathematics Theses
Given a sign pattern matrix M composed of two sub-patterns A and B connected by a 1-separation, we provide a formula that relates the minimum rank of M to the minimum rank of some small variations of A and B.
Jackknife Empirical Likelihood For The Variance In The Linear Regression Model, Hui-Ling Lin
Jackknife Empirical Likelihood For The Variance In The Linear Regression Model, Hui-Ling Lin
Mathematics Theses
The variance is the measure of spread from the center. Therefore, how to accurately estimate variance has always been an important topic in recent years. In this paper, we consider a linear regression model which is the most popular model in practice. We use jackknife empirical likelihood method to obtain the interval estimate of variance in the regression model. The proposed jackknife empirical likelihood ratio converges to the standard chi-squared distribution. The simulation study is carried out to compare the jackknife empirical likelihood method and standard method in terms of coverage probability and interval length for the confidence interval of …
Jackknife Empirical Likelihood Inference For The Absolute Mean Deviation, Xueping Meng
Jackknife Empirical Likelihood Inference For The Absolute Mean Deviation, Xueping Meng
Mathematics Theses
In statistics it is of interest to find a better interval estimator of the absolute mean deviation. In this thesis, we focus on using the jackknife, the adjusted and the extended jackknife empirical likelihood methods to construct confidence intervals for the mean absolute deviation of a random variable. The empirical log-likelihood ratio statistics is derived whose asymptotic distribution is a standard chi-square distribution. The results of simulation study show the comparison of the average length and coverage probability by using jackknife empirical likelihood methods and normal approximation method. The proposed adjusted and extended jackknife empirical likelihood methods perform better than …
Classification For 2011-2012 Bangladesh Integrated Household Survey By Iterative Clustering Technique, Wen Zhou
Mathematics Theses
In this project, the raw data from a survey, 2011-2012 Bangladesh Integrated Household Survey, is cleaned. Based on the research purpose of the collaborator, important variables are extracted and principal component analysis is used to form a new data set. The iterative clustering technique is applied to the new data set to classify the households involved in the survey into different categories. The categories are interpreted as reflecting the different economic activities in Bangladesh.
Small Improvement To The Kolmogorov-Smirnov Test, Xing Dong
Small Improvement To The Kolmogorov-Smirnov Test, Xing Dong
Mathematics Theses
The Kolmogorov-Smirnov (K-S) test is widely used as a goodness-of-fit test. This thesis consists of two parts to describe ways to improve the classical K-S test in both 1-dimensional and 2-dimensional data. The first part is about how to improve the accuracy of the classical K-S goodness-of-fit test in 1-dimensional data. We replace the p-values estimated by the asymptotic distribution with near-exact p-values. In the second part, we propose two new methods to increase power of the widely used 2-dimensional two-sample Fasano and Franceschini test. Simulation studies show the new methods are significantly more powerful than the Fasano and …
Antiretroviral Regimens In Hiv-Infected Adults Receiving Medical Care In The United States: Medical Monitoring Project, 2009, Yunfeng Tie
Mathematics Theses
Effective antiretroviral therapy (ART) is essential for viral suppression (VS) in HIV-infected patients. However, there is a lack of nationally representative data on types of ART regimens used and their impact on VS. This thesis used self-reported interview and abstracted medical record from 2009 Medical Monitoring Project (MMP) to study ART regimen type and related health outcomes. Results showed that 88.6% of HIV-infected adults in care was prescribed ART, and about half took regimens designated as ‘preferred’ according to U.S ART guidelines. Among MMP participants prescribed ART, 62.7% achieved durable VS, 77.8% achieved recent VS, 83.5% were 100% dose-adherent, and …
Identification Of Differential Gene Pathways With Sparse Principal Component Analysis, Yichao Yin
Identification Of Differential Gene Pathways With Sparse Principal Component Analysis, Yichao Yin
Mathematics Theses
The development of the technology makes it possible to measure large amount of genes expressions simultaneously. Since biological functions are mostly coordinated by multiple genes, called “gene pathway”, it is interesting to identify differential gene pathways which are associated with clinical phenotype. Principal component analysis has been proposed to identify differential gene pathways in several literatures, while sparse principal component analysis (SPCA) has not drawn any attention. We proposed to use SPCA to identify differential gene pathways. The results show that, comparing to PCA, SPCA could identify more differential expressed gene pathways, especially when the higher-order interactions among genes are …