A bootstrapped sequential probability ratio test for signal processing applications

A new algorithm is presented that combines the bootstrap and the generalized sequential probability ratio test. The latter replaces all unknown parameters with suitable estimates so that the test statistic is subject to uncertainty. The question of how to choose the decision thresholds for the generalized sequential probability ratio test such that it fulfills given constraints on the error probabilities is still open. We propose to address this problem not by adjusting the thresholds, but by bootstrapping the estimates of the unknown parameters and constructing confidence intervals for the test statistic. The stopping rule of the test is then defined in terms of this confidence interval instead of the test statistic itself. The proposed procedure is reliable and admits the beneficial properties of sequential tests in terms of the expected number of samples. It can hence be useful for applications where making observations is expensive or time critical, as is often the case in Internet-of-Things, data analytics or wireless communications.