Approximations in Sequential Rules for Discrimination of Complex Hypotheses and Their Precision in the Problem of Signal Detection from Postdetector Data

Exact formulas are derived for the performance characteristic and average duration of Wald's sequential rule for discrimination of complex hypotheses that take into account threshold jumps by the logarithm of the probability ratio. Approximations of the characteristics of Wald's rule and the asymptotically minimax sequential rule are provided and compared. The accuracy of the found approximations in limiting situations is illustrated by the example of detection of a Gaussian signal from the results of preliminary processing.