Jackknife Empirical Likelihood Inference for the Absolute Mean Deviation

• Main Author: meng, xueping
• Format: Others
• Published: Digital Archive @ GSU 2013
• Subjects: Confidence interval; Coverage probability; Jackknife empirical likelihood
• Online Access: http://digitalarchive.gsu.edu/math_theses/132; http://digitalarchive.gsu.edu/cgi/viewcontent.cgi?article=1135&context=math_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 other methods for symmetric and skewed distributions. We use real data sets to illustrate the proposed jackknife empirical likelihood methods.