On Optimal Stopping Problems in Sequential Hypothesis Testing

After a brief survey of a variety of optimal stopping problems in sequential testing theory, we give a unified treatment of these problems by introducing a general class of loss functions and prior distributions. In the context of a one-parameter exponential family, this unified treatment leads to relatively simple sequential tests involving generalized likelihood ratio statistics or mixture likelihood ratio statistics. The latter have been used by Robbins in his development of power-one tests, whose optimality properties are also discussed in this connection.