Author

Da ChenFollow

Date of Award

5-8-2020

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Yichuan Zhao

Second Advisor

Jun Kong

Third Advisor

Jing Zhang

Abstract

The calculation of correlation coefficient can be inaccurate with the existence of distortion measurement errors. Such measurement errors could act in an additive or multiplicative fashion. To study the additive model, previous research has shown residual-based estimation of correlation coefficients. The powerful tool of empirical likelihood has been used to construct the confidence interval for the correlation coefficient. However, the methods so far only perform well when sample sizes are large. With small sample size situations, the coverage of EL can be below 90%. On the basis of previous research, this article proposes new methods of interval estimation for the correlation coefficient using jackknife empirical likelihood, mean jackknife empirical likelihood and adjusted jackknife empirical likelihood. For better performance with small sample sizes, we also propose adjusted mean jackknife empirical likelihood and mean adjusted empirical likelihood. The simulation results show the best performance with mean adjusted jackknife empirical likelihood when the sample sizes are as small as 25. Real data analyses are used to illustrate the proposed approach.

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