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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 …
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 …