On Random Distortion Testing Based Sequential Non-Parametric Hypothesis Testing*

In this work, we propose a new method for sequential binary hypothesis testing. The approach is non-parametric in the sense that it does not assume any knowledge of signal distributions under each hypothesis. The proposed framework is based on Random distortion testing (RDT) which addresses the problem of testing whether or not a random signal, deviates by more than a specified tolerance, $\tau$, from a fixed value, $\xi_{0}$. We first state the problem setup and then discuss earlier approaches to solve the problem. We then propose a new sequential algorithm, T-SeqRDT, which is shown to control the probabilities of error while reducing the number of samples required to make a decision compared to the fixed-sample-size version of RDT. Finally, via simulations we compare T-SeqRDT to other algorithms and show its robustness compared to standard likelihood ratio based approaches.