Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Empirical Likelihood Confidence Intervals For Generalized Lorenz Curve, Nelly E. Belinga-Hill
Empirical Likelihood Confidence Intervals For Generalized Lorenz Curve, Nelly E. Belinga-Hill
Mathematics Theses
Lorenz curves are extensively used in economics to analyze income inequality metrics. In this thesis, we discuss confidence interval estimation methods for generalized Lorenz curve. We first obtain normal approximation (NA) and empirical likelihood (EL) based confidence intervals for generalized Lorenz curves. Then we perform simulation studies to compare coverage probabilities and lengths of the proposed EL-based confidence interval with the NA-based confidence interval for generalized Lorenz curve. Simulation results show that the EL-based confidence intervals have better coverage probabilities and shorter lengths than the NA-based intervals at 100p-th percentiles when p is greater than 0.50. Finally, two real examples …
Inference For Cox's Regression Model Via A New Version Of Empirical Likelihood, Ali Jinnah
Inference For Cox's Regression Model Via A New Version Of Empirical Likelihood, Ali Jinnah
Mathematics Theses
Cox Proportional Hazard Model is one of the most popular tools used in the study of Survival Analysis. Empirical Likelihood (EL) method has been used to study the Cox Proportional Hazard Model. In recent work by Qin and Jing (2001), empirical likelihood based confidence region is constructed with the assumption that the baseline hazard function is known. However, in Cox’s regression model the baseline hazard function is unspecified. In this thesis, we re-formulate empirical likelihood for the vector of regression parameters by estimating the baseline hazard function. The EL confidence regions are obtained accordingly. In addition, Adjusted Empirical Likelihood (AEL) …
Empirical Likelihood-Based Nonparametric Inference For The Difference Between Two Partial Aucs, Yan Yuan
Empirical Likelihood-Based Nonparametric Inference For The Difference Between Two Partial Aucs, Yan Yuan
Mathematics Theses
Compare the accuracy of two continuous-scale tests is increasing important when a new test is developed. The traditional approach that compares the entire areas under two Receiver Operating Characteristic (ROC) curves is not sensitive when two ROC curves cross each other. A better approach to compare the accuracy of two diagnostic tests is to compare the areas under two ROC curves (AUCs) in the interested specificity interval. In this thesis, we have proposed bootstrap and empirical likelihood (EL) approach for inference of the difference between two partial AUCs. The empirical likelihood ratio for the difference between two partial AUCs is …
Empirical Likelihood Confidence Intervals For The Sensitivity Of A Continuous-Scale Diagnostic Test, Angela Elaine Davis
Empirical Likelihood Confidence Intervals For The Sensitivity Of A Continuous-Scale Diagnostic Test, Angela Elaine Davis
Mathematics Theses
Diagnostic testing is essential to distinguish non-diseased individuals from diseased individuals. More accurate tests lead to improved treatment and thus reduce medical mistakes. The sensitivity and specificity are two important measurements for the diagnostic accuracy of a diagnostic test. When the test results are continuous, it is of interest to construct a confidence interval for the sensitivity at a fixed level of specificity for the test. In this thesis, we propose three empirical likelihood intervals for the sensitivity. Simulation studies are conducted to compare the empirical likelihood based confidence intervals with the existing normal approximation based confidence interval. Our studies …