A Generalization of a Preliminary Testing Procedure for Pooling Data

This paper is concerned with a generalization of the sometimes-pool procedure for pooling two estimators which is based on a preliminary test of significance. A weighted estimator for one of the parameters is obtained by using weights which are determined by the observed value of the preliminary test statistic. The efficiencies of the weighting procedure and of the sometimes-pool procedure are compared for the special case where the estimators are normally distributed. Further, it is shown that the weighting procedure offers a greater degree of control over the disturbances which may result from pooling than does the sometimes-pool procedure. Some problems concerning the choice of a weighting function are discussed.