A Comparison of Some Confidence Intervals for Estimating the Kurtosis Parameter

Authors

Guensley JeromeFollow

Document Type

Thesis

Degree

Master of Science (MS)

Major/Program

Mathematical Sciences

First Advisor's Name

B. M. Golam Kibria

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

Florence George

Second Advisor's Committee Title

Committee Member

Third Advisor's Name

Wensong Wu

Third Advisor's Committee Title

Committee Member

Keywords

Kurtosis, Confidence Interval, Bootstrap, Simulation, Kurtosis Parameter, Kurtosis Estimator

Date of Defense

6-15-2017

Abstract

Several methods have been proposed to estimate the kurtosis of a distribution. The three common estimators are: g₂, G₂ and b₂. This thesis addressed the performance of these estimators by comparing them under the same simulation environments and conditions. The performance of these estimators are compared through confidence intervals by determining the average width and probabilities of capturing the kurtosis parameter of a distribution. We considered and compared classical and non-parametric methods in constructing these intervals. Classical method assumes normality to construct the confidence intervals while the non-parametric methods rely on bootstrap techniques. The bootstrap techniques used are: Bias-Corrected Standard Bootstrap, Efron’s Percentile Bootstrap, Hall’s Percentile Bootstrap and Bias-Corrected Percentile Bootstrap. We have found significant differences in the performance of classical and bootstrap estimators. We observed that the parametric method works well in terms of coverage probability when data come from a normal distribution, while the bootstrap intervals struggled in constantly reaching a 95% confidence level. When sample data are from a distribution with negative kurtosis, both parametric and bootstrap confidence intervals performed well, although we noticed that bootstrap methods tend to have smaller intervals. When it comes to positive kurtosis, bootstrap methods perform slightly better than classical methods in coverage probability. Among the three kurtosis estimators, G₂ performed better. Among bootstrap techniques, Efron’s Percentile intervals had the best coverage.

Identifier

FIDC001904

Recommended Citation

Jerome, Guensley, "A Comparison of Some Confidence Intervals for Estimating the Kurtosis Parameter" (2017). FIU Electronic Theses and Dissertations. 3489.
https://digitalcommons.fiu.edu/etd/3489