Confidence Interval For The Estimation of The Correlation Coefficient

Abstract

Pearson's ( ) is  a point estimator that estimates ( r ). The statistic ( ) is used to describe the linear relationship between two variables that are normally distributed. If  the  theoretical sampling distribution is not available, we will use the Monte Carlo (MC) procedure to approximate the true sampling distribution of Pearson's ( ). The goal  is used Monte Carlo that would improve the accuracy of the estimation of correlation coefficient. Then, variance reduction is used to improve the efficiency of Monte Carlo methods. In this study, the Monte Carlo, the Fisher’s z Method and the Bootstrap have been used for producing good approximate confidence intervals for the estimation of the correlation coefficient . Also, in this paper the coverage of confidence interval for the estimation of the correlation coefficient of the all methods have been used, and establish the average estimate of correlation coefficient, standard error, CIs and the width for the estimation of the correlation coefficient using the Monte Carlo (MC) Method. Finally, variance reduction  is used to reduce variability (e.g.  Importance Sampling)