Optimal Robust Sequential Tests of Circular Nonconforming Probability

We investigate the minimax nonparametric formulation of sequentially testing hypothesis on the circular nonconforming probability (CNP) that refers to the chance of the system missing a pre-specified 2D disk target.Such a problem occurs in the military science of ballistics, GPS, and GSM, etc., where we want to use as few as samples to assess the precision quality of the 2D system, but we do not make any parametric assumptions on the true underlying distributions for the observed raw data.We show that a Bernoulli sequential probability ratio test (SPRT) is optimal in the sense of minimizing the maximum expected sample sizes among all (fixed-sample or sequential) tests with the same or smaller Type I and Type II error probabilities.Since asymptotic theories in sequential analysis often assume small error probabilities, which are not always feasible in practice, we also propose algorithms to suitably design and implement Bernoulli SPRTs that are simple but useful for practitioners in real world applications.