Bootstrap based sequential probability ratio tests

We present a generalized sequential probability ratio test for composite hypotheses wherein the thresholds are updated in an adaptive manner based on the data recorded up to the current sample using the parametric bootstrap. The resulting test avoids the asymptotic assumption usually made in earlier works. The increase of the average sample number of the proposed method is not significant compared to the sequential probability ratio test which is based on known parameters, especially in a low SNR region. In addition, the probability of false alarm and the probability of missed detection are maintained below the preset values. A comparison shows that the thresholds based on the parametric bootstrap are in close agreement with the thresholds based on Monte-Carlo simulations.