Date of Award
Spring 5-10-2014
Degree Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
First Advisor
Yichuan Zhao
Abstract
Skewness and kurtosis are measures used to describe shape characteristics of distributions. In this thesis, we examine the interval estimates about the skewness and kurtosis by using jackknife empirical likelihood (JEL), adjusted JEL, extended JEL, traditional bootstrap, percentile bootstrap, and BCa bootstrap methods. The limiting distribution of the JEL ratio is the standard chi-squared distribution. The simulation study of this thesis makes a comparison of different methods in terms of the coverage probabilities and interval lengths under the standard normal distribution and exponential distribution. The proposed adjusted JEL and extended JEL perform better than the other methods. Finally we illustrate the proposed JEL methods and different bootstrap methods with three real data sets.
DOI
https://doi.org/10.57709/5517430
Recommended Citation
Zhang, Yan, "Jackknife Empirical Likelihood Inferences for the Skewness and Kurtosis." Thesis, Georgia State University, 2014.
doi: https://doi.org/10.57709/5517430