Truncated sequential probability ratio test

Abstract

It is well known that in the testing of a simple hypothesis H versus a simple alternative K, the sequential probability ratio test (SPRT) has the smallest average sample number (ASN) under H and K. Compared to the corresponding best fixed sample size (FSS) test, the saving in the average number of samples under H or K in the SPRT is significant. However, when the parameter values of the sample distribution lie between those hypothesized under H and K, the ASN for the SPRT can become much larger than the sample size of the corresponding FSS test, especially for small probabilities of error. It is shown here that a properly truncated SPRT can eliminate this undesirable feature. For small probabilities of error, truncating the SPRT at the sample size needed for the corresponding FSS test serves as a remedy, while the test is essentially unaffected when the samples are distributed according to H or K.