APPROXIMATING THE CHARACTERISTICS OF SEQUENTIAL TESTS
Joseph Glaz
James R. Kenyon
Abstract: In this paper the dependence structure inherent in the sequence of partial sums is
utilized to derive accurate approximations for the tail probabilities of the stopping time
associated with sequential tests for the normal mean. The approximations for these tail
probabilities are used to approximate the overall significance level, power function, expected
stopping time, and the variance of the stopping time associated with the sequential tests
discussed here. Moreover, after the testing procedure has been completed, the approximations
derived in this paper are used to evaluate -values and confidence intervals for the normal
mean. Numerical results are presented for the sequential probability ratio test and the
asymptotically optimal Bayes test.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -