LARGE-SAMPLE POOLING PROCEDURE FOR CORRELATION

The problem of simultaneous estimation of a set of correlations of bivariate normal populations is considered. The asymptotic properties of some shrinkage estimators in the case of a quadratic loss function are investigated. It is shown that the proposed positive-rule estimator uniformly dominates the usual and the shrinkage estimator in a setting of local alternatives. Furthermore, it is demonstrated analytically and numerically that the proposed shrinkage preliminary test estimator provides a wider range than the usual preliminary test estimator in which it dominates the classical estimator of correlation parameters. More importantly, the size of the preliminary test for the proposed shrinkage preliminary test estimator is appropriate.