An invariant sprt for identification

Abstract

We consider the problem of identifying a population with one of the two given populations. A sample is given from the population to be identified and from the other two populations we can sample either sequentially or non-sequentially. The populations are considered to be normal, differing only in their unknown means, and the common variance may be known or unknown. In the non-sequential case the HPKE (Holley, Preston, Kemperman, and Edwards) inequality yields partial monotonicity for the error probabilities of the best fixed sample invariant test. In the sequential case a truncated invariant SPRT is proposed as a solution, since the untruncated SPRT does not terminate with probability one Further a simple technique yields good bounds on the error probabi!ities Numerical comparisons with the fixed sample invariant test show that even though we are not in the i.i.d. situation, the truncated SPRT achieves subsantial savings. Some other numerical studies relating to the performance of this SPRT are also made here.

Keywords:

• invaniance
• truncated sequential probability ratio test
• HPKE inequality, Monte Carlo experiments