Abstract

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.

Information

Preprint No.SS-2024-0334
Manuscript IDSS-2024-0334
Complete AuthorsQunzhi Xu, Yajun Mei
Corresponding AuthorsQunzhi Xu
Emailsxuqunzhi66@gmail.com

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Acknowledgments

The authors would like to thank the reviewers, Associate Editor, and co-

Editors for their invaluable comments and encouragements. Y. Mei is partially supported by an NSF-DMS grant 2515158.

Supplementary Materials

This supplementary material provides detailed proof of Lemma 1 as well as

the proof of Theorem 1 under continuous case.

Supplementary materials are available for download.