On borrowing spread from auxiliary samples in the one-sample problem

Abstract

This study is concerned with the one-sample problem and the notion of how to use (borrow) information contained in one or more auxiliary samples. A variety of t-statistics and borrowning schemes is used to shed light on this area. It is found that if the data do not come from a Gaussian distribution then the traditional method of borrowing by root-mean-square need not be the best thing to do. (In fact, for Student's t-statistic it is never the best thing to do.) it is also shown that if one borrows wisely, substantial gains can be made for small sample sizes. Finally, if one places a premium on computational ease, then there are simple procedures that can do reasonably well under a variety of circumstances.