Jackknife empirical likelihood for the correlation coefficient with additive distortion measurement errors

The correlation coefficient is fundamental in advanced statistical analysis. However, traditional methods of calculating correlation coefficients can be biased due to the existence of confounding variables. Such confounding variables 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 (EL) 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 probability of EL, for instance, can be below 90% at confidence level 95%. On the basis of previous research, we propose 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 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.