Shrinkage estimation of a correlation coefficient and two examples with real life data-sets

Consider the problem of estimating the correlation coefficient of a bivariate normal distribution in a decision theoretic setup. Usually the population correlation coefficient is estimated by the sample correlation coefficient which is also the maximum likelihood estimator (MLE). In this article we have proposed several competing correlation estimators, and studied their performance in term of Pitman Nearness Criterion (PNC) as well as Stochastic Domination Criterion (SDC). A simple shrinkage version of the MLE seems to outperform the MLE in terms of both the above mentioned criteria. Finally, we have applied our proposed correlation estimators to two real life data sets to show their performance compared to the MLE.