Shrinkage estimation in pooling data for arbitrary populations
Syed Ejaz Ahmed, S. M. Khan · Environmetrics · 1991
Abstract The classical problem of pooling data of two independent random samples drawn possibly from two identical arbitrary populations is considered. Decision to pool the two samples or not is based on the outcome of the preliminary test and then a shrinkage technique is used. In an asymptotic setup, the distributional risks of the proposed estimators are derived and compared. This study reveals the robustness property of the proposed shrinkage preliminary test maximum likelihood estimator (SPTMLE) when the assumed restraints may not hold. It is shown that the proposed estimator provides a wider range than the usual preliminary test maximum likelihood estimator (PTMLE) in which it dominates the classical estimator. More importantly, the SPTMLE provides more meaningful size for the preliminary test.