On a Pooling Problem from the Statistical Decision Viewpoint

A problem is posed of how to divide a set of K independent random variables into a smaller number of mutually exclusive groups so that the groups are homogeneous. Following some ideas of Wald, a loss function is postulated from economic considerations; a Bayes solution to the problem is derived and the resulting least squares criterion applied to a numerical example. Some limitations of the approach are discussed; relationships to other work are indicated.