Truncated Sequential Non-Parametric Hypothesis Testing Based on Random Distortion Testing

Abstract

In this paper, we propose a new algorithm for sequential non-parametric hypothesis testing based on Random Distortion Testing (RDT). The data-based approach is non-parametric in the sense that the underlying signal distributions under each hypothesis are assumed to be unknown. Our previously proposed non-truncated sequential algorithm, Seq RDT, was shown to achieve desired error probabilities under a few assumptions on the signal model. In this paper, we show that the proposed truncated sequential algorithm, T- Seq RDT, requires even fewer assumptions on the signal model, while guaranteeing the error probabilities to be below pre-specified levels and at the same time makes a decision faster compared to its optimal fixed-sample-size counterpart, Block RDT. We derive bounds on the error probabilities and the average stopping times of the algorithm. Via numerical simulations, we compare the performance of T- Seq RDT with Seq RDT, Block RDT, sequential probability ratio test, and composite sequential probability ratio tests. We also show the robustness of the proposed approach compared with the standard likelihood ratio based approaches.