A class of nonparametric sequential tests

A class of nonparametric sequential tests is considered for testing a symmetric density under the hypothesis against a one-sided shift alternative. The test statistic at each observation is the sum of intermediate statistics obtained from the ranks within the most recent observations, where tn is a fixed ranking size. Excessive ranking of the data can be avoided with a proper choice of tn so that real-time implementation of the sequential rank test is feasible. Approximate expressions for the power and average sample number functions are given. Comparison with existing nonparametric tests is studied. Results show that the ranking size need not be very large in order that the performance of the proposed test be almost as good as sequential rank tests which require ranking of all the data.